Curriculum Vitae Dmitri Maximovitch Guitman (Gitman)

Transcrição

Curriculum Vitae
Dmitri Maximovitch Guitman (Gitman)
6 de setembro de 2010
Sumário
1
Dados Pessoais
1
2
Formação e Títulos Acadêmicos
2
3
Posições Acadêmicas
2
4
Atividades Didáticas
3
5
Orientação de estudantes e pós-doutorados
3
6
Livros publicados e em andamento
5
7
Artigos selecionados
7
8
Número de Publicações e de Citações Internacionais
10
9
Coordenação de Projetos e do Grupo de Pesquisa
11
10 Resumo dos principais resultados cientícos obtidos
11
10.1 Teoria quântica de campos com campos de fundo externos . . . . . . . . . . . . . . . . .
12
10.2 Teoria geral de sistemas com vínculos e sua quantização
16
. . . . . . . . . . . . . . . . . .
10.3 Soluções exatas das equações de onda relativísticas e teoria das extensões auto-adjuntas
19
10.4 Integrais de trajetória; teoria de grupos em mecânica quântica relativística e teoria de
campos; métodos semiclássicos e estados coerentes
. . . . . . . . . . . . . . . . . . . . .
23
10.5 Modelos clássicos e pseudoclássicos de partículas relativísticas e sua quantização . . . . .
26
10.6 Teoria dos spins altos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
28
10.7 Teoria de sistemas de dois e quatro níveis e aplicações à computação quântica . . . . . .
29
10.8 Mecânica quântica e teoria de campos nos espaços não comutativos . . . . . . . . . . . .
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10.9 Estatística quântica
10.10 Outros assuntos
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
31
1 Dados Pessoais
Data e local de Nascimento: 2 de julho de 1944, Tashkent, Usbequistão - URSS.
Brasileiro naturalizado
Idiomas: Russo, Inglês, Português e Alemão
Endereço: Instituto de Física da USP, Departamento de Física Nuclear, Instituto de Física, Universidade
de São Paulo, C.P. 66318, CEP 05315-970, São Paulo, SP, Brasil
Telefone: 55-11-3091-6948.
E-mail: [email protected], [email protected]
Homepage: http://www.dfn.if.usp.br/pesq/tqr/pt/gitman
CV Lattes: http://lattes.cnpq.br/7459553192735157
Bolsista de produtividade do CNPq na modalidade/nível: PQ-1A.
1
2 Formação e Títulos Acadêmicos
•
1961-1966: Bacharelado e Mestrado - Departamento de Física da Universidade Estadual de Tomsk
- Rússia. Recebeu medalha e o diploma vermelho. Tese de mestrado:
Integral Equations for
Distribution Functions in Statistical Mechanics.
•
1966-1969: Doutorado, Universidade Estadual de Tomsk - Rússia. 1969: Título PhD - Candidato
em Ciências Físicas e Matemáticas, obtido com a tese
Variational Principles in Quantum
Statistics - Universidade Estadual de Tomsk, Rússia. Diploma MFM No. 011435, State Higher
Attestation Commission, Moscou, 16 de janeiro de 1970. Pareceres ociais favoráveis recebidos
dos Professores V.L. Pokrovsky - Landau Institute, Chernogolovka: M. Gaigasian- Universidade
Estadual de Tomsk e Prof.
A.A. Sokolov, Universidade Estadual de Moscou.
Este título foi
reconhecido pela USP em 5/06/1996 como equivalente ao Título de Doutor, conforme
documento no. 94.1.997.43.4.
•
1975: Grau acadêmico de
Docente da cadeira de Física Teórica e Matemática. Diploma
MDC no. 096071, Higher Attestation Commission, Moscou 1 de abril de 1976.
•
1979: Obteve o título de
Doctor in Sciences , (mais alto grau cientíco em Física e Matemática
concedido na Rússia) com a tese
Problems of External Fields in Quantum Electrodyna-
mics , Instituto de Física Nuclear de Novosibirsk. Diploma FM No. 001066, Higher Attestation
Commission, Moscou, 18 de abril de 1980. Pareceres ociais favoráveis recebidos dos professores:
F.A. Berezin, Universidade Estadual de Moscou. Prof. B.N. Baier, Instituto de Física Nuclear,
Novosibirsk, Prof. V.N. Barbashov, Instituto Internacional de Pesquisas Nucleares, Dubna, e Prof.
V.I. Manko, Instituto de Física Lebedev, Moscou.
Esse título foi reconhecido pela USP em
5/06/1996 como equivalente ao título de Livre-Docência, conforme documento No.
94.1.1005.43.5.
•
1981: Grau acadêmico de
Professor Catedrático da cadeira de Física Teórica . Aprovado
pelo Russian Ministry of Higher Education.
Diploma PR No.
007429, Higher Attestation
Commission, Moscou, 26 de junho, 1981.
3 Posições Acadêmicas
•
1969-1970:
Professor Assistente no Departamento de Física - Tomsk Institute of Automation
Control Systems and Radio Engineering (TIASUR), Tomsk, Rússia.
•
1970-1975:
Professor Associado no Departamento de Física - Tomsk Institute of Automation
Control Systems and Radio Engineering, Tomsk, Rússia.
•
1975-1985: Professor Catedrático da Cadeira de Análise Matemática do Tomsk State Pedagogical
University (TSPU), Tomsk, Rússia.
•
1985-1992:
Professor Titular do Departamento de Matemática do Moscow Institute of Radio
Engineering, Electronics and Automation (MIREA), Moscou, Rússia.
•
1992-1996: Professor Colaborador, RDIDP, nível MS-6 no Departamento de Física Matemática,
Instituto de Física - Universidade de São Paulo, Brasil.
•
1996-1998:
Professor Associado, RDIDP, nível MS-5 no Departamento de Física Matemática,
Instituto de Física - Universidade de São Paulo, Brasil.
•
1998-: Professor Titular, RDIDP, nível MS-6 no Departamento de Física Nuclear, Instituto de
Física - Universidade de São Paulo, Brasil.
2
4 Atividades Didáticas
1 em cursos de
Desde 1969, ministrou cursos na graduação e pós-graduação em diversas universidades
graduação e pós graduação.
Na Rússia
1. Física Geral, 1969-1975, TIASUR
2. Mecânica Quântica, 1970-1975, TIASUR
3. Teoria Quântica do Estado Sólido, 1972-1975, TIASUR
4. Eletrodinâmica, 1970-1975, TIASUR
5. Física Matemática, 1976-1985, TSPU
6. Cálculo Matemático, 1976-1982, TSPU, MIREA
7. Teoria de Grupos, 1976-1985, TSPU
8. Teoria Quântica de Campos, 1976-1985, TSU
9. Quantização de Sistemas com Vínculos, 1980-1984, TSU
10. Relatividade Geral, 1970-1975, TSU
No Brasil
1. Teoria de sistemas com vínculos, 1992, 1994, 2000, 2009, USP, para alunos de pós graduação.
2. Integrais de trajetória em Mecânica Quântica e Teoria de Campos, 1993, 1994, 1997, 1999, USP,
para alunos de pós-graduação.
3. Relatividade Geral, 1993, 1996, 2007, 2009, USP, para alunos de pós-graduação.
4. Introdução à Relatividade Geral, 1995, 2000, 2008, USP, para alunos de graduação.
5. Mecânica Quântica II, 1995, USP, para alunos de graduação.
6. Física Geral IV, 1996, 2005, USP, para alunos de graduação.
7. Física Geral III, 1998, 2001, 2002, 2003, 2006, 2007, USP, para alunos de graduação.
8. Física Geral I, 2004, 2005, USP, para alunos de graduação.
5 Orientação de estudantes e pós-doutorados
Orientou os seguintes alunos:
Mestrados
1. P.V. Bozrikov, Tese de Mestrado: Berson model in QED (Tomsk State University, Tomsk, 1969)
2. P.M. Lavrov. Tese de Mestrado: Exact solvable models in QED (Tomsk State University, Tomsk,
1972)
3. V.M. Shachmatov. Tese de Mestrado: Charged particles in strong electromagnetic elds, (Tomsk
State University, Tomsk, 1974)
1
TIASUR-Tomsk Institute of Automation Control Systems and Radio Engineering; TSPU-Tomsk State Pedagogical
Universtity; MIREA-Moscow Institute of Radio Engineering, Electronics and Automation; TSU-Tomsk State University;
USP-University of Sao Paulo
3
4. S.P. Gavrilov.
Tese de Mestrado:
Particle creation in QED (Tomsk State University, Tomsk,
1978)
5. I.M. Lichtzier.
Tese de Mestrado:
Some quantum processes in external electromagnetic elds,
(Tomsk State University, Tomsk, 1984)
6. V.P. Barashev.
Tese de Mestrado: Reduction formulas in QED with unstable vacuum, (Tomsk
State University, Tomsk, 1985)
7. João Luis Meloni Assirati. Dissertação de Mestrado: Generalização covariante do ordenamento
de Weyl e quantização da partícula, (Universidade de São Paulo, São Paulo, Setembro 2001)
8. Mario Cesar Baldiotti, Dissertação de Mestrado: Estados Quânticos de um Elétron em um Campo
Magnético Uniforme, (Universidade de São Paulo, São Paulo, Maio 2002)
9. Rodrigo Fresneda, Dissertação de Mestrado: Quantização da partícula relativística espinorial em
2+1
dimensões, (Universidade de São Paulo, São Paulo, Agosto 2003)
10. Tiago Carlos Adorno de Freitas, Dissertação de Mestrado: Particula Espinorial (Pseudo)Classica e
Quântica em Espacos Commutativos e Não Comutativos. (Universidade de São Paulo, São Paulo,
Agosto 2009)
Doutorados
1. P.V. Bozrikov. Tese de Doutorado: Motion of an electron in the quantized electromagnetic plane
wave, (Tomsk State University, Tomsk, 1973);
2. P.M. Lavrov.
Tese de Doutorado:
Processes with an electron in the quantized electromagnetic
plane wave, (Tomsk State University, Tomsk, 1975);
3. Sh.M. Shvartsman.
Tese de Doutorado:
Some quantum processes in intensive electromagnetic
elds, (Tomsk State University, Tomsk, 1975);
4. V.M. Shachmatov.
Tese de Doutorado: Quantum processes with a relativistic charged particle,
interacting with strong electromagnetic eld, (Azerbaijan State University, Baku, 1978);
5. S.P. Gavrilov. Tese de Doutorado : Some problems of QED with an external eld, creating pairs,
(Moscow State University, Moscow, 1981);
6. I.M. Lichtzier.
Tese de Doutorado: Green's functions and one-loop eective action in external
gauge and gravitational elds, (Tomsk State University, Tomsk, 1988);
7. M.D. Noskov. Tese de Doutorado: Problems of QED with intensive external elds, (Tomsk State
University, Tomsk, 1989);
8. V.P. Barashev. Tese de Doutorado: Problems of QED with unstable vacuum, (Tomsk State University, Tomsk, 1989);
9. A.L. Shelepin. Tese de Doutorado: Group methods in quantum theory and coherent states, (Lebedev Physical Institute, Moscow, 1990).
10. Antonio Edson Gonçalves.
Tese de Doutorado:
Modelos Pseudoclássicos e suas quantizações,
(Universidade de São Paulo, 1995).
11. Wellington da Cruz. Tese de Doutorado: Representações via integrais de trajetória de propagadores
de partículas relativísticas, (Universidade de São Paulo, 1995).
12. Paulo Barbosa Barros. Tese de Doutorado: Algumas aplicações de integrais de trajetória grass-
mannianas na teoria quântica moderna, (Universidade de São Paulo, São Paulo, 1998)
13. Jose Nemecio Acosta Jara. Tese de Doutorado: Teoria quântica da radiação de partículas em um
campo magnético solenoidal, (Universidade de São Paulo, São Paulo, dezembro 2002)
4
14. Andrei Smirnov, Tese de Doutorado: A equação de Dirac com uma sobreposição do campo de
Aharonov-Bohm e um campo magnético uniforme colinear, (Universidade de São Paulo, São Paulo,
agosto 2004)
15. Mario Cesar Baldiotti. Tese de Doutorado: Estudo analítico e soluções exatas da equação de spin,
(Universidade de São Paulo, São Paulo, junho 2005)
16. Rodrigo Fresneda, Tese de Doutorado: Alguns problemas de quantização em teorias com fundos
não-abelianos e em espaços-tempo não-commutativos, (Universidade de São Paulo, São Paulo,
otubro 2008)
17. Vladislav Kupriyanov, Tese de Doutorado, Quantização de sistemas não-lagrangianos e mecânica
quântica não-comutativa, (Universidade de São Paulo, São Paulo, março 2009)
18. João Luis Meloni Assirati, Tese de Doutorado: Quantização covariante de sistemas mecânicos,
(Universidade de São Paulo, São Paulo, abril 2010)
19. Damiao P. Meira Filho, Tese de Doutorado: Movimento quântico e semiclássico em um campo de
um magnético-solenóide, (Universidade de São Paulo, São Paulo, otubro 2010)
Pós-doutorados
1. 1997-1999: Geza Fulop, Projeto: Reparametrization invariace and zero Hamiltonian phenomenon
2. 1997-1998: Anton Galajinsky, Projeto: Classical and quantum dynamics of the theory of super-
symmetric extended objects
3. 1997-1998:
Alexei Deriglazov, Projeto:
Problems of covariant formulation and quantization of
constraint systems
4. 1998-2000:
Alexei Shelepin, Projeto:
Methods of harmonic analysis and of generalized regular
representation for Poincare group in various dimensions
5. 2002-2009: Pavel Moshin, Projeto: Problems of Lagrangian
and Hamiltonian BRST quantization
of gauge theories
6. 2004: Andrei Smirnov, Projeto: The study of vacuum polarization in backgrounds with singularities
7. 2005-: Mário César Baldiotti, Projeto: Estudo de sistemas de dois e quatro níveis, em andamento;
8. 2010-: Rodrigo Fresneda, Projeto: Quantização de teorias em espaços-tempo não-commutativos,
em andamento.
9. 2010- Nelson Yokomizo, Projeto: Creacao de particulas em campo de Coulomb com
andamento.
6 Livros publicados e em andamento
1.
Exact Solutions of the Relativistic Wave Equations
com V. G. Bagrov, I. M. Ternov et al.
Nauka, Novosibirsk (1982)
144 páginas (em Russo)
5
Z > 137,
em
2.
Canonical Quantization of Fields with Constraints
com I. V. Tyutin
Nauka, Moscow (1986)
3.
Exact Solutions of Relativistic wave Equations
com V. G. Bagrov
Kluwer Acad. Publish., Dordrecht, Boston, London (1990)
321 páginas
4.
Quantum Electrodynamics with Unstable Vacuum
com E. S. Fradkin e Sh. M. Shvartsman
Nauka, Moscow (1991)
5.
Quantum Electrodynamics with Unstable Vacuum
com E. S. Fradkin, Sh. M. Shvartsman
Springer-Verlag, Berlin, Heidelberg, New-York, London, Paris, Hong-Kong, Barcelona, (1991)
300 páginas
6.
Quantization of Fields with Constraints
com I. V. Tyutin
Springer-Verlag, Berlin, Heidelberg, New-York, London, Paris, Hong-Kong, Barcelona, (1990)
292 páginas
7. D. M. Gitman, I. V. Tyutin, and B. Voronov:
Physical Observables in Non-trivial Quantum
Systems (Constructing self-adjoint operators and solving spectral problems), a ser punlicado em
2011 por
Birkhäuser (Springer Verlag).
8. V. G. Bagrov, D. M. Gitman: Relativistic Wave Equations with External Electromagnetic Fields
and their Solutions, a ser publicado em 2012 por Kluwer Acad. Publish.
6
9. D. M. Gitman, I. V. Tyutin: Classical Theory of Constrained Systems, a ser publicado em 2013
por
Springer Verlag.
7 Artigos selecionados
Os artigos listados a seguir são uma seleção de suas publicações mais importantes, juntamente com os
respectivos abstracts :
1. D.M. Gitman and A. Shelepin, Field on Poincaré Group and Quantum Description of Orientable
Objects, Europ. Physical Journal C, 61, Issue1 (2009)111, DOI 10.1140/epjc/s10052-009-0954-x.
We propose an approach to the quantum-mechanical description of relativistic orientable objects.
It generalizes Wigner's ideas concerning the treatment of nonrelativistic orientable objects (in
particular, a nonrelativistic rotator) with the help of two reference frames (space-xed and bodyxed). A technical realization of this generalization (for instance, in
3+1
dimensions) amounts
to introducing wave functions that depend on elements of the Poincaré group
G.
A complete set
of transformations that test the symmetries of an orientable object and of the embedding space
belongs to the group
Π = G × G.
generalized regular representation of
All such transformations can be studied by considering a
G
in the space of scalar functions on the group,
x ∈ G/Spin(3, 1) as well
Z ∈ Spin(3, 1). In particular,
depend on the Minkowski space points
given by the elements
z
of a matrix
f (x, z),
that
as on the orientation variables
the eld
f (x, z)
is a generating
function of usual spin-tensor multicomponent elds. In the theory under consideration, there are
four dierent types of spinors, and an orientable object is characterized by ten quantum numbers.
We study the corresponding relativistic wave equations and their symmetry properties.
2. S.P. Gavrilov and D.M. Gitman, Consistency Restrictions on Maximal Electric-Field Strength in
Quantum Field Theory, Phys. Rev. Lett. 101, 130403(4) (2008).
QFT with an external background can be considered as a consistent model only if backreaction is
relatively small with respect to the background. To nd the corresponding consistency restrictions
on an external electric eld and its duration in QED and QCD, we analyze the mean energy density
of quantized elds for an arbitrary constant electric eld
T.
E,
acting during a large but nite time
Using the corresponding asymptotics with respect to the dimensionless parameter
eET 2 ,
one
can see that the leading contributions to the energy are due to the creation of paticles by the
electric eld. Assuming that these contributions are small in comparison with the energy density
of the electric background, we establish the above-mentioned restrictions.
3. B.L. Voronov, D.M. Gitman, and I.V. Tyutin, The Dirac Hamiltonian with a superstrong Coulomb
eld, Theoretical and Mathematical Physics, 150(1) (2007) 34-72 (Translated from Teoreticheskaya i Matematicheskaya Fizika,
150, No. 1, pp.41-84, 2007).
We consider the quantum-mechanical problem of a relativistic Dirac particle moving in the Coulomb eld of a point charge
Ze.
In the literature, it is often declared that a quantum-mechanical
description of such a system does not exist for charge values exceeding the so-called critical charge
with
Z = α−1 = 137
based on the fact that the standard expression for the lower bound state
energy yields complex values at overcritical charges. We show that from the mathematical standpoint, there is no problem in dening a self-adjoint Hamiltonian for any value of charge. What
is more, the transition through the critical charge does not lead to any qualitative changes in the
mathematical description of the system. A specic feature of overcritical charges is a non uniqueness of the self-adjoint Hamiltonian, but this non uniqueness is also characteristic for charge values
less than the critical one (and larger than the subcritical charge with
√
Z = ( 3/2)α−1 = 118).
We present the spectra and (generalized) eigenfunctions for all self-adjoint Hamiltonians.
The
methods used are the methods of the theory of self-adjoint extensions of symmetric operators and
the Krein method of guiding functionals. The relation of the constructed one-particle quantum
mechanics to the real physics of electrons in superstrong Coulomb elds where multiparticle eects
may be of crucial importance is an open question.
4. S.P. Gavrilov, D.M. Gitman, One-loop energy-momentum tensor in QED with electric-like back-
ground, Phys. Rev. D78, 045017(35) (2008).
7
We have obtained nonperturbative one-loop expressions for the mean energy-momentum tensor
and current density of Dirac's eld on a constant electric-like background. One of the goals of this
calculation is to give a consistent description of back-reaction in such a theory. Two cases of initial states are considered: the vacuum state and the thermal equilibrium state. First, we perform
calculations for the vacuum initial state. In the obtained expressions, we separate the contributions due to particle creation and vacuum polarization. The latter contributions are related to
the HeisenbergEuler Lagrangian. Then, we study the case of the thermal initial state. Here, we
separate the contributions due to particle creation, vacuum polarization, and the contributions
due to the work of the external eld on the particles at the initial state. All these contributions
are studied in detail, in dierent regimes of weak and strong elds and low and high temperatures.
The obtained results allow us to establish restrictions on the electric eld and its duration under
which QED with a strong constant electric eld is consistent. Under such restrictions, one can
neglect the back-reaction of particles created by the electric eld. Some of the obtained results
generalize the calculations of HeisenbergEuler for energy density to the case of arbitrary strong
electric elds.
5. D.M. Gitman, I.V. Tyutin, Symmetries and physical functions in general gauge theory, Int.
Mod. Phys.A,
J.
21, No.2 (2006) pp. 327-360.
The aim of the present article is to describe the symmetry structure of a general gauge (singular)
theory, and, in particular, to relate the structure of gauge transformations with the constraint
structure of a theory in the Hamiltonian formulation. We demonstrate that the symmetry structure
of a theory action can be completely revealed by solving the so-called symmetry equation. We
develop a corresponding constructive procedure of solving the symmetry equation with the help
of a special orthogonal basis for the constraints.
Thus, we succeed in describing all the gauge
transformations of a given action. We nd the gauge charge as a decomposition in the orthogonal
constraint basis. Thus, we establish a relation between the constraint structure of a theory and
the structure of its gauge transformations.
In particular, we demonstrate that, in the general
case, the gauge charge cannot be constructed with the help of some complete set of rst-class
constraints alone, because the charge decomposition also contains second-class constraints. The
above-mentioned procedure of solving the symmetry equation allows us to describe the structure
of an arbitrary symmetry for a general singular action. Finally, using the revealed structure of
an arbitrary gauge symmetry, we give a rigorous proof of the equivalence of two denitions of
physicality condition in gauge theories:
one of them states that physical functions are gauge-
invariant on the extremals, and the other requires that physical functions commute with FCC
(the Dirac conjecture).
6. S.P. Gavrilov, D.M. Gitman, and J.L. Tomazelli, Density matrix of a quantum eld in a particle-
creating background, Nucl. Phys. B 795 [FS] (2008) 645-677.
We examine the time evolution of a quantized eld in external backgrounds that violate the
stability of vacuum (particle-creating backgrounds). Our purpose is to study the exact form of the
nal quantum state (the density operator at the nal instant of time) that has emerged from a
given arbitrary initial state (from a given arbitrary density operator at the initial time instant) in
the course of evolution. We nd a generating functional that allows one to obtain density operators
for an arbitrary initial state. Averaging over states of the subsystem of antiparticles (particles), we
obtain explicit forms of reduced density operators for the subsystem of particles (antiparticles).
Analyzing one-particle correlation functions, we establish a one-to-one correspondence between
these functions and the reduced density operators. It is shown that in the general case a presence
of bosons (e.g., gluons) in the initial state increases the creation rate of the same type of bosons.
We discuss the question (and its relation to the initial stage of quark-gluon plasma formation)
whether a thermal form of one-particle distribution can appear even if the nal state of the
complete system is not in thermal equilibrium.
In this respect, we discuss some cases when
pair-creation by an electric-like eld can mimic the one-particle thermal distribution. We apply
our technics to some QFT problems in slowly varying electric-like backgrounds: electric, SU(3)
chromoelectric, and metric. In particular, we analyze the time and temperature behavior of the
mean numbers of created particles, provided that the eects of switching the external eld on and
o are negligible. It is demonstrated that at high temperatures and in slowly varying electric elds
8
the rate of particle-creation is essentially time-dependent.
7. D. M. Gitman, and I.V. Tyutin, Hamiltonization of theories with degenerate coordinates, Nucl.
Phys. B630 (3) (2002) pp. 509-527.
We consider a class of Lagrangian theories where part of the coordinates does not have any time
derivatives in the Lagrange function (we call such coordinates degenerate). We advocate that it
is reasonable to reconsider the conventional denition of singularity based on the usual Hessian
and, moreover, to simplify the conventional Hamiltonization procedure.
In particular, in such
a procedure, it is not necessary to complete the degenerate coordinates with the corresponding
conjugate momenta.
8. V.G. Bagrov, D.M. Gitman, A. Levin, and V.B. Tlyachev, Aharonov-Bohm Eect in cyclotron
and synchrotron radiations, Nucl. Phys. B605 (2001) 425-454.
We study the impact of Aharonov-Bohm solenoid on the radiation of a charged particle moving
in a constant uniform magnetic eld.
With this aim in view, exact solutions of Klein-Gordon
and Dirac equations are found in the magnetic-solenoid eld. Using such solutions, we calculate
exactly all the characteristics of one-photon spontaneous radiation both for spinless and spinning
particle. Considering non-relativistic and relativistic approximations, we analyze cyclotron and
synchrotron radiations in detail. Radiation peculiarities caused by the presence of the solenoid
may be considered as a manifestation of Aharonov-Bohm eect in the radiation. In particular, it
is shown that new spectral lines appear in the radiation spectrum. Due to angular distribution
peculiarities of the radiation intensity, these lines can in principle be isolated from basic cyclotron
and synchrotron radiation spectra.
9. S.P. Gavrilov, D.M. Gitman, Quantization of Point-Like Particles and Consisitent Relativistic
Quantum Mechanics, Int. J. Mod. Phys. A15 (2000) 4499-4538.
We revise the problem of the quantization of relativistic particle models (spinless and spinning),
presenting a modied consistent canonical scheme. One of the main point of the modication is
related to a principally new realization of the Hilbert space.
It allows one not only to include
arbitrary backgrounds in the consideration but to get in course of the quantization a consistent
relativistic quantum mechanics, which reproduces literally the behavior of the one-particle sector
of the corresponding quantum eld.
In particular, in a physical sector of the Hilbert space a
complete positive spectrum of energies of relativistic particles and antiparticles is reproduced, and
all state vectors have only positive norms.
10. D.M. Gitman, Path integrals and pseudoclassical description for spinning particles in arbitrary
dimensions, Nucl. Phys. B 488 (1997) 490-512.
The propagator of a spinning particle in external Abelian eld and in arbitrary dimensions is
presented by means of a path integral. The problem has distinct solutions in even and odd dimensions. In even dimensions the representation is just a generalization of one in four dimensions (it
has been known before). In this case a gauge invariant part of the eective action in the path integral has a form of the standard (Berezin-Marinov) pseudoclassical action. In odd dimensions the
solution is presented for the rst time and, in particular, it turns out that the gauge invariant part
of the eective action diers from the standard one. We propose this new action as a candidate to
describe spinning particles in odd dimensions. Studying the hamiltonization of the pseudoclassical
theory with the new action we show that the operator quantization leads to adequate minimal
quantum theory of spinning particles in odd dimensions. Finally the consideration is generalized
for the case of the particle with anomalous magnetic moment.
11. S.P. Gavrilov and D.M. Gitman, Vacuum instability in external elds, Phys.Rev.D
53 (1996) 7162-
7175.
We study particles creation from the vacuum by external electric elds, in particular, by elds,
which are acting for a nite time, in the frame of QED in arbitrary space-time dimensions. In all the
cases special sets of exact solutions of Dirac equation (IN- and OUT- solutions) are constructed.
Using them, characteristics of the eect are calculated.
the vacuum instability is presented.
The time and dimensional analysis of
It is shown that the distributions of particles created by
quasiconstant electric elds can be written in a form which has a thermal character and seams
9
to be universal, i.e. is valid for any theory with quasiconstant external elds. Its application, for
example, to the particles creation in external constant gravitational eld reproduces the Hawking
temperature exactly.
12. D.M. Gitman and S.I. Zlatev, Spin factor in path integral representation for Dirac propagator in
external eld, Phys. Rev. D55 (1997) 7701-7714.
We study the spin factor problem both in
3 + 1 and 2 + 1 dimensions which are essentially dierent
for spin factor construction. Doing all Grassmann integrations in the corresponding path integral
representations for Dirac propagator we get representations with spin factor in arbitrary external
eld. Thus, the propagator appears to be presented by means of bosonic path integral only. In
3+1
dimensions we present a simple derivation of spin factor avoiding some unnecessary steps in the
original brief letter (Gitman, Shvartsman, Phys. Lett.
B318 (1993) 122) which themselves need
some additional justication. In this way the meaning of the surprising possibility of complete
integration over Grassmann variables gets clear. In
2+1 dimensions the derivation of the spin factor
is completely original. Then we use the representations with spin factor for calculations of the
propagator in some congurations of external elds. Namely, in constant uniform electromagnetic
eld and in its combination with a plane wave eld.
13. E.S. Fradkin and D.M. Gitman Path integral representation for the relativistic particle propagators
and BFV quantization, Phys. Rev. D 44 (1991) 3230-3236.
The path-integral representations for the propagators of scalar and spinor elds in an external
electromagnetic eld are derived. The Hamiltonian form of such expressions can be interpreted
in the sense of Batalin-Fradkin-Vilkovisky quantization of one-particle theory.
The Lagrangian
representation as derived allows one to extract in a natural way the expressions for the corresponding gauge-invariant (reparametrization- and supergauge-invariant) actions for pointlike scalar
and spinning particles. At the same time, the measure and ranges of integrations, admissible gauge
conditions, and boundary conditions can be exactly established.
14. E.S. Fradkin and D.M. Gitman, Furry picture for quantum electrodynamics with pair-creating
external eld, Fortschr. Phys. 29 (1981) 381-411.
In the paper the perturbation theory is constructed for QED, for which the interaction with the
external pair-creating eld is kept exactly.
causal electron propagator is found.
An explicit expression for the perturbation theory
Special features of usage of the unitarity conditions for
calculating the total probabilities of radiative processes in the case are discussed. Exact Green
functions are introduced and the functional formulation is discussed.
Perturbation theory for
calculating the mean values of the Heisenberg operators, in particular, of the mean electromagnetic
eld is built in the case under consideration.
Eective Lagrangian which generates the exact
equation for the mean electromagnetic eld is introduced.
Functional representations for the
generating functionals introduced in the paper are discussed.
15. D.M. Gitman, Processes of arbitrary order in quantum electrodynamics with a pair-creating exter-
nal eld, Journ. Phys. A 10 (1977) 2007-2020.
Dyson's perturbation theory analogue for quantum electrodynamical processes with arbitrary initial and nal states in an external eld creating pairs has been discussed. The interaction with
the eld is taken into account exactly. The possibility of using Feynman diagrams, together with
modied correspondence rules, for the representation o the above mentioned processes has been
demonstrated.
8 Número de Publicações e de Citações Internacionais
•
208 artigos completos publicados em periódicos.
•
26 trabalhos completos publicados em anais de congressos.
•
17 capítulos de livros publicados.
•
6 livros publicados.
10
•
257 publicações no total.
•
Comlete "citation index"(according to Google Scholar): 2281.
9 Coordenação de Projetos e do Grupo de Pesquisa
• Quantization problems and QED in strong elds
Projeto temático da FAPESP, processo: 1996/07134-8
Vigência: 1996-2002
• Alguns problemas atuais em teoria quântica de campos
• Quantização e problemas da teoria quântica de campos
• Problems of quantization of non-trivial classical models
Programa CAPES/COFECUB, N
o 566/07
• Aspectos modernos da quantização por estados coerentes
Programa FAPESP/CNRS, Processo: 2009/54771-2
•
Coordenador do grupo de pesquisa
Quanta (Teoria quântica relativística)
Departamento Fisica Nuclear do IFUSP, homepage: http://www.dfn.if.usp.br/pesq/tqr .
10 Resumo dos principais resultados cientícos obtidos
Obteve resultados nas seguintes àreas de investigação:
•
Teoria quântica de campos com campos de fundo externos
•
Teoria de sistemas com vínculos e sua quantização
•
Soluções exatas das equações de onda relativísticas e teoria das extensões auto-adjuntas
•
Integrais de trajetória; teoria de grupos em mecânica quântica relativística e teoria de campos;
métodos semiclássicos e estados coerentes
•
Modelos clássicos e pseudoclássicos de partículas relativísticas e sua quantização
•
Teoria de spins altos
•
Teoria de sistemas de dois e quatro níveis e aplicações à computação quântica
•
Mecânica quântica e teoria de campos nos espaços não commutativos
•
Estatística quântica
•
Outros assuntos
Abaixo, são detalhados os resultados em cada área, juntamente com os artigos em que os resultados
foram publicados.
11
10.1
•
Teoria quântica de campos com campos de fundo externos
Foi elaborada uma formulação geral de QED com campos externos que violam a estabilidade do
vácuo. Em particular, foi construída uma teoria de perturbação com relação à interação radioativa,
levando-se em conta exatamente a interação com campos externos (análoga ao quadro de Furry
em QED com vácuo estável) [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21,
22, 24, 23, 25, 26, 27, 28, 29, 31, 32].
•
Os resultados obtidos para campos eletromagnéticos externos foram generalizados para QFT com
campos de fundo não-abelianos e gravitacionais nos artigos [33, 34, 16, 35, 20, 36, 37, 38, 56, 47,
61, 58, 57].
•
Foram apresentados vários cálculos do efeito de criação de partículas. Por exemplo, o cenário temporal da criação de partículas em campo elétrico [1, 39, 40], cálculos em congurações complicadas
de campos externos (combinação de campos elétrico, magnético e de onda plana) [2, 41, 42, 43],
cálculos do efeito da criação de partículas em teorias de dimensão alta [40, 47]. Foi apresentada
nos artigos [44, 45, 46, 28, 62] uma construção geral da matriz densidade de partículas criadas
por campos externos e foi descoberta pela primeira vez uma relação estreita entre a criação de
partículas em campos eletromagnéticos externos e em campos gravitacionais [44, 28].
•
Foi calculada a expressão não perturbativa de um loop para o valor médio do tensor de energiamomento do campo de Dirac em campo elétrico e magnético. Asim, foi obtida a back reaction
no campo externo, além das partículas criadas [63, 64, 65, 66].
•
Foram calculados processos radiativos em vários campos eletromagnéticos [48, 49, 50, 51, 52, 53,
54, 43, 55, 59, 60, 67].
•
Foram escritos os livros Quantum
Electrodynamics with Unstable Vacuum [30, 31], que
sintetizam alguns desses resultados.
Referências
[1] V.G. Bagrov, D.M. Gitman and Sh.M. Shvartsman, Concerning the production of electron-positron
pairs from vacuum, Zh. Eksp. Teor. Fiz. 68 (1975) 392-399; Sov. Phys.-JETP, Vol. 41, No. 2 (1975)
191-194.
[2] V.G. Bagrov, S.P. Gavrilov, D.M. Gitman and Sh.M. Shvartsman, Creation of Boson Pairs from
Vacuum, Izw. VUZov Fizika 18 No. 3 (1975) 71-74; (Soviet Physics Journal 18 NO.3 (1975) 351354)
[3] V.G. Bagrov, D.M. Gitman and V.A. Kuchin, External eld in quantum electrodynamics and co-
herent states In Actual problems of theoretical physics (Moscow State University Publ., Moscow,
1976) pp. 334-342.
[4] D.M. Gitman, Quantum processes in an intensive electromagnetic eld. I. Izw. VUZov Fizika (Sov.
Phys. Journ.)
10 (1976) 81-86.
[5] D.M. Gitman, Quantum processes in an intensive electromagnetic eld. II. Izw. VUZov Fizika (Sov.
Phys. Journ.)
10 (1976) 86-92.
[6] D.M. Gitman S.P. and Gavrilov, Quantum processes in an intensive electromagnetic eld creating
pairs. III. Izw. VUZov Fizika (Sov. Phys. Journ.) I (1977) 94-99.
[7] D.M. Gitman, Processes of arbitrary order in quantum electrodynamics with a pair-creating external
eld, Journ. Phys. A 10 (1977) 2007-2020.
[8] D.M. Gitman, Processes of arbitrary order in quantum electrodynamics with pair-creating external
eld, In Quantum electrodynamics with external eld (Tomsk State University, Tomsk, 1977) pp.
132-149.
12
[9] E.S. Fradkin and D. M. Gitman, Quantum electrodynamics with intense external eld, Preprint
MIT (1978) 1-58.
[10] S.P. Gavrilov, D.M. Gitman and Sh. M. Shvartsman, Green's functions in external electric eld,
Sov. Journ. Nucl. Phys. (Yadern. Fizika)
29 (1979) 1097-1109
[11] S.P. Gavrilov, D. M. Gitman and Sh.M. Shvartsman, Green's functions in external electric eld and
its combination with magnetic eld and plane-wave eld, Sov. Journ. Nucl. Phys. (Yadern. Fizika),
29 (1979) 1392-1405.
[12] S.P. Gavrilov, D.M. Gitman and Sh.M. Shvartsman, Green's functions in external electric eld and
its combination with magnetic eld and plane-wave eld, Kratk. Soob. Fiz. (Lebedev Inst.), No. 2
(1979) 22-26.
[13] E.S. Fradkin and D.M. Gitman, Problems of quantum electrodynamics with intensive eld, Preprint
PhIAN (Lebedev Institute),
106 (1979) 1-62.
[14] E.S. Fradkin and D.M. Gitman, Problems of quantum electrodynamics with intensive eld. (Appen-
dix), Preprint PhIAN (Lebedev Institute), 107 (1979) 1-40.
[15] E.S. Fradkin and D.M. Gitman, Problems of quantum electrodynamics with intensive eld creating
pairs, Central research inst. for Phys., Budapest, REKI197983, pp. 1-105.
[16] I.L. Buchbinder and D.M. Gitman, A denition of the vacuum in curved space-time, Izw. VUZov
Fizika (Sov. Phys. Journ.)
7 (1979) 16-21.
[17] S.P. Gavrilov, D.M. Gitman and Sh.M. Shvartsman, The unitarity relation in quantum electrody-
namics with pair-creating external eld, Izw. VUZov Fizika (Sov. Phys. Journ. 257-260) 3 (1980)
93-96 .
[18] S.P. Gavrilov and D.M. Gitman, Furry picture for scalar quantum electrodynamics with intensive
pair-creating eld, Izw. VUZov Fizika (Sov. Phys. Journ. 491-496) 6 (1980) 37-42 .
[19] E.S. Fradkin and D.M. Gitman, Furry picture for quantum electrodynamics with pair-creating ex-
ternal eld, Fortschr. Phys. 29 (1981) 381-411.
[20] I.L. Buchbinder, E.S. Fradkin and D.M. Gitman, Generating functional in quantum eld theory
with unstable vacuum, Preprint PhIAN (Lebedev Institute), 138 (1981).
[21] D.M. Gitman and V.A. Kuchin, Generating functional of mean eld in quantum electrodynamics
with unstable vacuum, Izw. VUZov Fizika (Sov. Phys. Journ.) 10 (1981) 80-84.
[22] S.P. Gavrilov, D.M. Gitman and E.S. Fradkin, Quantum electrodynamics at nite temperature in
presence of an external eld, violating the vacuum stability, Sov. Journal Nucl. Phys. (Yadernaja
Fizika),
46 (1987) 172-180.
[23] E.S. Fradkin, D.M. Gitman and Sh.M. Shvartsman, Optical theorem in quantum electrodynamics
with unstable vacuum, Fortschr. Phys. 36 (1988) 643-669.
[24] V.G. Bagrov, V.P. Barashev, D.M. Gitman, and Sh.M. Shvartsman, Green functions in exter-
nal electromagnetic eld, in Collection Quantum processes in intense external elds, pp. 101-111,
(Shteentza, Kishenev, 1987) (3B348b88)
[25] V.P. Barashev, D.M. Gitman, E.S. Fradkin and Sh.M. Shvartsman, Peculiarities of reduction for-
mulas in quantum electrodynamics with unstable vacuum, Preprint PhIAN (Lebedev Institute) 177
(1988) 1-26.
[26] D.M. Gitman, E.S. Fradkin and Sh.M. Shvartsman, Quantum electrodynamics with external eld,
violating the vacuum stability, Trudy PhIAN (Proceedings of Lebedev Institute, Moscow), 193
(1989) 3-207.
13
presence of an external eld, violating the vacuum Stability, Trudy PhIAN (Proceedings of Lebedev
Institute, Moscow),
193 (1989) 208-221.
[28] V.P. Barashev, E.S. Fradkin, D.M. Gitman and Sh.M. Shvartsman, The problems of QED with
unstable vacuum. Reduction formulas. The density matrix of particles creating in an external eld,
Trudu PhIAN (Proceedings of Lebedev Institute, Moscow)
201 (1990) 74-94.
[29] S.P. Gavrilov and D.M. Gitman, Interpretation of external eld and external current in QED, Sov.
Journ. Nucl. Phys. (Yadern. Fizika)
51 (1990) 1644-1654.
[30] E.S. Fradkin, D.M. Gitman and Sh.M. Shvartsman,
Quantum Electrodynamics with Unstable
Vacuum (Springer-Verlag, Berlin Heidelberg New-York London Paris Hong-Kong Barcelona, 1991)
pp. 1-300.
[31] D.M. Gitman, E.S. Fradkin and Sh.M. Shvartsman,
Vacuum , (Nauka, Moscow, 1991) pp. 1294.
Quantum Electrodynamics with Unstable
[32] S.P.Gavrilov, D.M.Gitman, Furry Representation for Fermions, interacting with an external gauge
eld, Izw. VUZov Fizika (Russian Phys. Journ.) No 4 (1995) 102-108.
[33] I.L. Buchbinder and D.M. Gitman, A method of calculation of quantum processes probabilities in
external gravitational elds. I, Izw. VUZov Fizika (Sov. Phys. Journ.) 3 (1979) 90-95.
[34] I.L. Buchbinder and D.M. Gitman, A method of calculation of quantum processes probabilities in
external gravitational elds. II, Izw. VUZov Fizika (Sov. Phys. Journ.) 4 (1979) 55-61.
[35] I.L. Buchbinder, E.S. Fradkin and D.M. Gitman, Quantum electrodynamics in curved space-time,
Fortschr. Phys.
29 (1981) 187-218.
[36] I.L. Buchbinder, E.S. Fradkin and D.M. Gitman, Quantum electrodynamics in curved space-time,
201 (1990) 3373.
[37] S.P. Gavrilov and D.M. Gitman, Problems of an External Field in Non-Abelian Gauge Theory on
an example of the standard
SU (2) × U (1)
model, Preprint MIT, CTP # 1995 (1991) 1-53; Problems
of an External Field in Non-Abelian Gauge Theory, Proceedings of the First International Sakharov
Conference on Physics, Sakharov Memorial Lectures in Physics Vol.2 (1991) 187-194, Edited by
L.V. Keldysh and V.Ya. Fainberg, Nova Science Publishers, Inc.
[38] S.P.Gavrilov, D.M.Gitman, Green's Functions and Matrix Elements in Furry Picture for Electro-
weak Theory with non-Abelian External Field, Izw. VUZov Fizika (Russian Phys. Journ.) 36, No 5
(1993) 448-452.
[39] D.M. Gitman, V.M. Shachmatov and Sh.M. Shvartsman, Pair creation in the electric eld, acting
for a nite time, Izw. VUZov Fizika (Sov. Phys. Journ.) 4 (1975) 23-29.
[40] S.P. Gavrilov and D.M. Gitman, Vacuum instability in external elds, Phys. Rev. D
53 (1996)
7162-7175
[41] V.G. Bagrov, D.M. Gitman and Sh.M. Shvartsman, Pair creation from vacuum by an electromagne-
tic eld in the zero-plane formalism, Sov. Journ. Nucl. Phys. (Yadern. Fizika), 23 (1976) 394-400.
[42] S.P. Gavrilov and D.M. Gitman, Processes of pair-creation and scattering in constant eld and
plane-wave eld, Izw. VUZov Fizika (Sov. Phys. Journ.) 5 (1981) 108-111.
[43] D.M. Gitman, M.D. Noskov and Sh.M. Shvartsman, Quantum eects in a combination of a constant
uniform eld and a plane wave eld, Intern. Journ. Mod. Phys. A 6 (1991) 44374489.
[44] V.P. Frolov and D.M. Gitman, Density matrix in quantum electrodynamics, equivalence principle
and Hawking eect, Journ. Phys. A 15 (1978) 1329-1333.
14
[45] D.M. Gitman V.P. and Frolov, Density matrix in quantum electrodynamics and Hawking eect,
Sov. Journ. Nucl. Phys. (Yadern. Fizika),
28 (1978) 552-557.
[46] I.L. Buchbinder, D.M. Gitman and V.P. Frolov, Density matrix for particle-creation processes in
external eld, Izw. VUZov Fizika (Sov. Phys. Journ. 529-533) 6 (1980) 77-81.
[47] S.P. Gavrilov, D.M. Gitman, and A.E. Gonçalves, QED in external eld with space-time uniform
invariants: Exact solutions, Journ. Math. Phys. 39 (1998) 3547-3567
[48] V.G. Bagrov, P.V. Bozrikov, D.M. Gitman, Yu.I. Klimenko and A.I. Khudomjasov, Radiation of
Neutral Fermion with Electric and Magnetic Moments in Constant and Uniform External Electromagnetic Fields, Izw. VUZov Fizika 17 No. 6 (1974) 150-151; (Soviet Physics Journal 17 No. 6
(1974) 890-891)
[49] V.G. Bagrov, P.V. Bozrikov, D.M. Gitman, Yu.I. Klimenko and A.I. Khudomjasov, Electromagnetic
Wave Scattering at a Neutral Fermion Possessing Magnetic and Electric Moments, Izw. VUZov
Fizika
17 No. 7 (1974) 138-139; (Soviet Physics Journal 17 No. 7(1974) 1072-1028)
[50] V.G. Bagrov, D.M. Gitman, A.A. Sokolov et al., Radiation of relativistic electrons, moving in the
nite length ondulator, Journ. Technic. Fiz. XLV, 9 (1975) 1948-1953.
[51] V.G. Bagrov, D.M. Gitman and V.N. Rodionov et al., Eect of a strong electromagnetic wave on
the radiation emitted by weakly excited electrons, moving in magnetic eld, Zh. Eksp. Teor. Fiz. 71
(1976) 433-439.
[52] Yu.Yu. Volfengaut, S.P. Gavrilov, D.M. Gitman and Sh.M. Shvartsman, Radiative processes in
external pair-creating electromagnetic eld, Sov. Journ. Nucl. Phys. (Yadern. Fizika) 33 (1981)
743-757.
[53] S.P. Gavrilov and D.M. Gitman, Vacuum radiative processes in pair-creating elds, Izw. VUZov
Fiz.
9 (1982) 10-12 (Sov. Phys. Journ. 9 (1982) 775-778.)
[54] S.P. Gavrilov and D.M. Gitman, Radiative processes with an electron in constant homogeneous eld
, Izw. VUZov Fiz.
10 (1982) 102-106 (Sov. Phys. Journ. 10 (1982) 968-972.)
[55] D.M. Gitman, S.D. Odintsov and Yu.I. Shil'nov, Chiral symmetry breaking in
d=3
NJL model in
external gravitational and magnetic elds, Phys. Rev. D 54, No 4 (1996) 2968-2970
[56] S.P. Gavrilov, D.M. Gitman and S.D. Odintsov, Quantum Scalar Fields in the FRW Universe with
a Constant Electromagnetic Background, Int. J. Mod. Phys. A12 (1997) 4837-4867
[57] S.P. Gavrilov and D.M. Gitman, Quantum processes in FRW Universe with external electromagnetic
eld, Proceedings 8th Lomonosov Conference on Elementary Particle Physics (25-30 August 1997,
Moscow, Russia), Ed. A.I. Studenikin, (Int. Centre for Advanced Studies, Moscow 1999) 105-109
[58] S.P. Gavrilov, D.M. Gitman, and A.E. Gonçalves, Quantum Spinor Field in FRW Universe with
Constant Electromagnetic Background, Int.J.Mod.Phys.A16, No.26 (2001) 4235-4259
[59] I. Brevik, D.M. Gitman and S.D. Odintsov, The eective potential of gauged NJL model in a
magnetic eld, Gravitation and Cosmology, 3 (1997) 100-104
[60] I. Brevik, D.M. Gitman, and S.D. Odintsov, The Eective Potential of Gauged NJL Model in
Magnetic Field, in Proceedings of 1996 International Workshop PERSPECTIVES OF STRONG
COUPLING GAUGE THEORIES, (Nagoya, 13-16 November 1996, Japan), Editors J. Nishimura
and K. Yamawaki, (World Sci. Singapore, 1997) pp. 208-214
[61] S.P. Gavrilov, D.M. Gitman, The Proper-Time representation of Spinor Green Functions in FRW
Universe with Electromagnetic Background and some Applications of Them, Proceedings of Forth
Alexander Friedmann International Seminar on Gravitation and Cosmology, St. Petersburg, Russia,
June 17-25, 1998/editors: Yu.N. Gnedin [et al]- Campinas, SP: UNICAMP/IMECC, 1999, pp.268273
15
[62] S.P. Gavrilov, D.M. Gitman, and J.L. Tomazelli, Density matrix of a quantum eld in a particle-
creating background, Nucl. Phys. B 795 [FS] (2008) 645-677
[63] S.P. Gavrilov, D.M. Gitman, One-loop energy-momentum tensor in QED with electric-like back-
ground, Phys. Rev. D78, 045017(35) (2008)
[64] S.P. Gavrilov and D.M. Gitman, Energy-momentum tensor in thermal strong-eld QED with uns-
table vacuum, arXiv:0710.3933; J. Phys. A: Math. Theor. 41 (2008) 164046.
[65] S.P. Gavrilov and D.M. Gitman, Consistency Restrictions on Maximal Electric-Field Strength in
Quantum Field Theory, Phys. Rev. Lett. 101, 130403(4) (2008)
[66] S.P. Gavrilov, D.M. Gitman, On Schwinger Mechanism for Gluon Pair Production in the Presence
of Arbitrary Time Dependent Chromo-Electric Field, Europ. Physical Journal C, 64, Issue 1 (2009)
81; DOI: 10.1140/epjc/s10052-009-1135-7
[67] M. Bordag, I.V. Fialkovsky, D.M. Gitman, and D.V. Vassilevich, Casimir interaction between a
perfect conductor and graphene, described by the Dirac model, Phys. Rev. B 80, No.24 (2009)
10.2
•
Teoria geral de sistemas com vínculos e sua quantização
A estrutura do setor físico das teorias de gauge, de forma geral, foi exaustivamente descrita nas
formulações hamiltoniana e lagrangiana [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11]. Por exemplo, foi provado
pela primeira vez, que o número das transformações de gauge da ação é igual ao número de vínculos
primários de primeira classe na formulação hamiltoniana e que o número de variáveis não físicas
é igual ao número de vínculos de primeira classe.
•
Formulou-se pela primeira vez a hamiltonização e quantização dos sistemas singulares com derivadas altas [12, 13].
•
Foi formulada também pela primeira vez a hamiltonização e a quantização canônica de sistemas com vínculos dependentes do tempo e o método foi aplicado à quantização de sistemas com
hamiltonianas zero [14, 15, 16, 17, 18, 19].
•
Foram descritas todas as simetrias de uma teoria geral de gauge e, em particular, a forma das
transformações de gauge foi relacionada à estrutura de vínculos da mesma teoria em formulação hamiltoniana.
Obtivemos assim uma prova rigorosa da equivalência das duas denições de
grandezas físicas nas teorias de gauge: uma delas arma que as funções físicas são invariantes de
calibre nas estremais e a outra que as funções físicas são aquelas que comutam com os vínculos de
primeira classe (conjectura de Dirac) [20, 21, 22, 23, 24, 25, 26, 27].
•
Foi desenvolvida a chamada quantização triplética das teorias de gauge e uma extensão do esquema
BRSTanti BRST de superquantização covariante em coordenadas gerais [28, 29, 30, 31, 32, 33,
34, 35, 36].
•
Foi desenvolvida uma abordagem para quantizar sitemas com equações de movimento não lagrangianas [37, 38, 39, 40].
•
Os principais resultados foram publicados nos livros
Canonical Quantization of Fields with
Constraints [14], e Quantization of Fields with Constraints [15].
Referências
[1] D.M. Gitman and I.V. Tyutin, Canonical quantization of singular theories, Izw. VUZov Fizika (Sov.
Phys. Journ. 423-439)
5 (1983) 3-22.
[2] D.M. Gitman, Ya.S. Prager and I.V. Tyutin, Special canonical coordinates in constrained theories,
Izw. VUZov Fizika (Sov. Phys. Journ. 760-764)
8 (1983) 93-97.
16
[3] D.M. Gitman, S.L. Ljachovich, M.D. Noskov and I.V. Tyutin, Lagrangian formulation of Hamilto-
nian theory of general form with constraints, Proceedings of III Urmala Seminar, Urmala, 1985, v. 2
(Nauka, Moscow 1986) pp. 316-322.
[4] D.M. Gitman and I.V. Tyutin, Canonical quantization of gauge theories of special form, Izw. VUZov
3 (1986) 176-187.
[5] D.M. Gitman, S.L. Ljachovich, M.D. Noskov and I.V. Tyutin, Lagrangian formulation of Hamilto-
nian theory of general form with constraints, Izw. VUZov Fizika (Sov. Phys. Journ.) 3 (1986) 243-250.
[6] D.M. Gitman and I.V. Tyutin, The structure of gauge theories in the Lagrangian and Hamiltonian
formalisms, In Quantum eld theory and quantum statistics v. I, pp. 143164, Ed. by Batalin, Isham
and Vilkovisky (Adam Hilger, Bristol, 1987).
[7] D.M. Gitman and I.V. Tyutin, Canonical quantization of singular theories, In Group theoretical
methods in physics Proceedings of Second Zvenigorod Seminar Group Theoretical Methods Physics,
Zvenigorod, USSR, 1988, pp. 207-237.
[8] D.M. Gitman, P.M. Lavrov and I.V. Tyutin, Non-point transformation in constrained theories, Journal Phys. A
23 (1990) 41-51.
[9] D.M. Gitman, Canonical and D-transformations in theories with constraints, Int.J.Theor.Phys.
35,
No.1 (1996) 87-99
[10] D. M. Gitman, and I.V. Tyutin, Hamiltonization of theories with degenerate coordinates, Nucl.
Phys. B630 (3) (2002) pp. 509-527
[11] D. M. Gitman, and I.V. Tyutin, Hamiltonian Formulation of Theories with Degenerate Coordinates ,
Proceedings of 3-rd International Sakharov Conference on Physics, Moscow, Russia, June 24-29, 2002,
Vol.II, Editors A. Semikhatov, M. Vasiliev, V. Zaikin (Scientic World Publ. 2003) pp. 54-63
[12] D.M. Gitman, S.L. Ljachovich and I.V. Tyutin, Hamiltonian formalism of theories with higher
derivatives, Izw. VUZov Fizika (Sov. Phys. Journ. 730-735) 8 (1983) 61-66.
[13] D.M. Gitman, S.L. Ljachovich and I.V. Tyutin, Canonical quantization of Yang-Mills theory with
higher derivatives, Izw. VUZov Fizika (Sov. Phys. Journ.) 7 (1985) 37-40.
[14] D.M. Gitman and I.V. Tyutin,
Canonical quantization of elds with constraints
(Nauka,
Moscow, 1986) pp. 1-216.
Quantization of Fields with Constraints pp. 1291 (Springer-
Verlag, Berlin Heidelberg New-York London Paris Hong-Kong Barcelona, 1990).
[16] S.P. Gavrilov and D.M. Gitman, Quantization of Systems with Time-Dependent Constraints.
Example of Relativistic Particle in Plane Wave, Class. Quantum Grav. 10 (1993) 57-67.
[17] G. Fulop, D.M. Gitman and I.V. Tyutin, Reparametrization Invariace as Gauge Symmetry, Int. J.
Theor. Phys.
38 (1999) 1953-1980
[18] G. Fulop, D.M. Gitman, and I.V. Tyutin, Reparametrization Invariace and Zero Hamiltonian Phe-
nomenon, Proceedings 8th Lomonosov Conference on Elementary Particle Physics (25-30 August
1997, Moscow, Russia), Ed. A.I. Studenikin, (Int. Centre for Advanced Studies, Moscow 1999) 64-69
[19] G. Fulop, D.M. Gitman, and I.V. Tyutin,
Reparametrization Invariance and Zero Hamiltonian
Phenomenon, in Topics in Theoretical Physics II, Festschrift for Abraham H. Zimerman Ed. H.
Aratyn, L.Ferreira, J. Gomes, (IFT/UNESP-São Paulo-SP-Brazil-1998) pp. 286-295
[20] D. M. Gitman, and I.V. Tyutin, Constraint reorganization consistent with Dirac procedure, Michael
Marinov Memorial Volume: Multiple Facets of Quantization and Supersymmetry, ed. M. Olshanetsky
and A. Vainstein (World Publishing, Singapore 2002) pp.184-204
17
[21] D. M. Gitman, and I.V. Tyutin, Fine Structure of Constraints in Hamiltonian Formulation, Gravitation & Cosmology,
8, No.1-2 (2002) 138-140
[22] B. Geyer, D.M. Gitman, and I.V. Tyutin, Canonical form of Euler-Lagrange equations and gauge
symmetries, J. Phys. A36 (2003) 6587-6609
[23] B. Geyer, D.M. Gitman, and I.V. Tyutin, Reduction of Euler-Lagrange equations in general gauge
theories with external elds, Proceedings of Sixth Workshop (The University of Oklahoma, Norman,
OK USA September 15-19, 2003) on QUANTUM FIELD THEORY UNDER THE INFLUENCE OF
EXTERNAL CONDITIONS, Ed. K.A. Milton, (Rinton Press 2004) pp.276 - 281.
[24] D.M. Gitman, I.V. Tyutin, General quadratic gauge theory. Constraint structure, symmetries, and
physical functions, J. Phys. A: Math. Gen. 38 (2005) 5581-5602.
[25] D.M. Gitman, I.V. Tyutin, Symmetries in Constrained Systems, Resenhas IME-USP, Vol. 6, U
2116 2/3 (2004) pp. 187-198
[26] D.M. Gitman, I.V. Tyutin, Symmetries and physical functions in general gauge theory, Int. J. Mod.
Phys.A,
21, No.2 (2006) pp. 327-360
[27] D.M. Gitman, I.V. Tyutin, Symmetries of Dynamically Equivalent Theories, Brasilian Journal of
Physics,
36, no.1A (2006) pp. 132-140
[28] B. Geyer, D.M. Gitman, and P.M. Lavrov A modied scheme of triplectic quantization, Mod. Phys.
Lett.
A14 (1999) pp. 661-670
[29] B. Geyer, D.M. Gitman, and P.M. Lavrov, Triplectic quantization of gauge theories, Theor. Math.
Phys.
123, No.3 (2000) 813-820
[30] B. Geyer, D.M. Gitman, and P.M. Lavrov, Covariant Quantization with Extended BRST Symmetry,
Proceedings of International Seminar Physical Variables in Gauge Theories, Dubna,September 21-25,
Russia, 1999, Ed. by A.Khvedelidze, M.Lavelle, D.McMullan, and V.Pervushin, Dubna, 2000, pp.118128
[31] B. Geyer, D.M. Gitman, P. Lavrov, P. Moshin, On Problems of the Lagrangian Quantization of
W3 -gravity,
Int.J.Mod.Phys.
A18, No.27 (2003) 5099-5125
[32] B. Geyer, D.M. Gitman, P. Lavrov, P. Moshin, Supereld Extended BRST Quantization in General
Coordinates, Int.J.Mod.Phys.A19 (2004) pp.737-750
[33] D.M. Gitman, P.Yu. Moshin, J.L. Tomazelli, On supereld covariant quantization in general coor-
dinates, Eur. Phys. J. C44 (2005) 591-598
[34] D.M. Gitman, P.Yu. Moshin, A.A. Reshetnyak, Local Supereld Lagrangian BRST Quantization,
J. Math. Phys.
46:072302 (2005)
[35] D.M. Gitman, P.Yu. Moshin, and A.A. Reshetnyak, An embedding of the BV quantization into an
N=1 local supereld formalism, Publicação IFUSP - 1609/2005, hep-th/0507046, Phys. Lett. B 621
(2005) pp. 295-308
[36] D.M. Gitman , P.Yu. Moshin, A.A. Reshetnyak, Reducible gauge theories in local supereld Lagran-
gian BRST quantization, Brazilian Journal of Physics, 37 (2007) no. 4
[37] D. Gitman and V.G. Kupriyanov, Canonical quantization of non-Lagrangian theories and its ap-
plication to damped oscillator and radiating point-like charge, Eur. Phys. J. C50 (2007) 691-700
[38] D. Gitman and V.G. Kupriyanov, Quantization of Theories with non-Lagrangian Equations of
Motion, Journal of Math. Sciences 141 (2007) 1399-1406
[39] D.M. Gitman, V.G. Kupriyanov, Action principle for so-called non-Lagrangian systems, PoS
(IC2006) 016 (2006) pp 1-11
[40]
D.M. Gitman and V.G. Kupriyanov, The action principle for a system of dierential equations, J.
Phys. A: Math. Theor. 40 (2007) 10071-10081.
18
10.3
Soluções exatas das equações de onda relativísticas e teoria das extensões
auto-adjuntas
•
Foi obtido e sistematicamente investigado pela primeira vez um grande número de novas classes
de soluções exatas de equações de onda relativística em campos externos. [1, 2, 3, 4, 5, 6, 7, 3, 11,
8, 9, 10, 11, 12, 13, 14, 15, 16, 13, 17, 21, 23, 24, 22, 18, 19, 20]
•
Foi sistematicamente estudado um novo modelo exato em QED (elétron interagindo com onda
plana quantizada) [23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 11, 12, 34].
•
Foram calculadas várias espécies de funções de Green de equações de onda relativísticas com
diferentes métodos, por exemplo através do conjunto de soluções exatas, do método de tempo
próprio de Schwinger e do método da integral de trajetória [35, 36, 37, 38, 39, 40, 42, 41, 43, 44,
45, 46, 47].
•
Alguns dos resultados da atividade acima estão sintetizados nos livros
Exact Solutions of Re-
lativistic Wave Equations [21, 27].
•
Estudamos detalhadamente novas soluções exatas de equações de onda relativísticas em
2+1
3+1
e
dimensões na combinação do campo Aharonov-Bohm solenóide e alguns campos elétricos e
magnéticos adicionais [48, 49, 50, 51, 52, 53, 54]. As soluções obtidas foram usadas no estudo do
efeito Aharonov-Bohm nos campos eletromagnéticos correspondentes [55, 56, 57, 58, 59, 60, 61,
62, 63].
•
Foi desenvolvida uma adaptação da teoria geral das extensões auto-adjuntas para uso em problemas físicos com várias aplicações [64, 65, 66, 67, 68, 69, 70].
Referências
[1] V.G. Bagrov, D.M. Gitman, V.N. Zadorozhny and Sh.M. Shvartsman, An Electron in the Field of
Two Classical Plane Waves Propagating in Slightly Dierent Diractions, Soviet Physics Journal 18
No. 1 (1975) 34-36)
[2] V.G. Bagrov, D.M. Gitman, P.M. Lavrov, V.N. Zadorozhny and V.N. Shapovalov, New exact solu-
tions of the Dirac equation. II., Sov. Phys. Journ. 4 (1975) 29-33.
[3] V.G. Bagrov, D.M. Gitman, P.M. Lavrov, V.N. Zadorozhny and V.N. Shapovalov, New exact solu-
tions of the Dirac equation. III., Sov. Phys. Journ. 7 (1975) 7-11.
[4] V.G. Bagrov, D.M. Gitman, A.G. Meshkov et al., New exact solutions of the Dirac equation. IV.
Izw. VUZov Fizika (Sov. Phys. Journ.)
8 (1975) 73-79.
[5] D.M. Gitman, V.M. Shachmatov and Sh.M. Shvartsman, Completeness and orthogonality on the
null-plane of one class of solutions of relativistic wave equations, Izw. VUZov Fizika (Sov. Phys.
Journ.)
8 (1975) 43-49.
[6] V.G. Bagrov, N.N. Bizov, D.M. Gitman et al., New exact solutions of the Dirac equation. V. Izw.
VUZov Fizika (Sov. Phys. Journ.)
9 (1975) 105-111.
[7] V.G. Bagrov, D.M. Gitman and A.V. Jushin, Solutions for the motion of an electron in electroma-
gnetic eld, Phys. Rev. D 12 (1975) 3200-3201.
[8] V.G. Bagrov, D.M. Gitman, A.G. Meshkov and V. N. Shapovalov, Supplement to the work New
exact solutions of the Dirac equation. II, III Izw. VUZov Fizika (Sov. Phys. Journ.) 1 (1977) 126-127.
[9] V.G. Bagrov, D.M. Gitman, A.V. Shapovalov and V.N. Shapovalov, New exact solutions of the Dirac
equation. VI Izw. VUZov Fizika (Sov. Phys. Journ.) 6 (1977) 105-114.
[10] V.G. Bagrov, D.M. Gitman, N.B. Suchomlin et al., New exact solutions of the Dirac equation. VII.
7 (1977) 46-51.
19
[11] V.G. Bagrov, D.M. Gitman, P.M. Lavrov and V.N. Zadorozhni, Characterictic features of exact
solutions of the problem of an electron in quantized eld of a plane wave, Izw. VUZov Fizika (Sov.
Phys. Journ.)
3 (1977) 7-14.
[12] V.G. Bagrov, D.M. Gitman and A. V. Shapovalov, Integrals of motion in the electron in quantized
plane-wave problem, Izw. VUZov Fizika (Sov. Phys. Journ.) 2 (1977) 116-121.
[13] V.G. Bagrov and D.M. Gitman, Exact solutions of the relativistic wave-equations in external eld,
In Quantum electrodynamics with external elds, (Tomsk State University, Tomsk, 1977) pp. 5-100.
[14] V.G. Bagrov, D.M. Gitman, V.N. Zadorozhni et al., New exact solutions of the Dirac equation.
VIII, Izw. VUZov Fizika (Sov. Phys. Journ.) 2 (1978) 13-18.
[15] V.G. Bagrov, D.M. Gitman, V.N. Zadorozhni et al., New exact solutions of the Dirac equation. IX,
3 (1978) 46-49.
[16] V.G. Bagrov, D.M. Gitman, V.N. Zadorozhni at al.: New exact solutions of the Dirac equation,
Izw. VUZov Fizika (Sov. Phys. Journ. 276-281)
4 (1980) 10-16.
[17] V.G. Bagrov, D.M. Gitman and V.N. Shapovalov, Electron motion in longitudinal electromagnetic
elds, J. Math. Phys. 23 (1982) 2558-2561.
[18] S.P. Gavrilov, D.M. Gitman, and J.L. Tomazelli, Comments on spin operators and spin-polarization
states of
2+1
fermions, Eur. Phys. J. C (2005) DOI: 10.1140/epjc/s2004-02026-9
[19] V.G. Bagrov, D.M. Gitman, Non-Volkov solutions for a charge in a plane wave, Annalen der Physik
14, 8 (2005) pp. 467-478
[20] V.G. Bagrov, M.C. Baldiotti, D.M. Gitman, Charged particles in crossed and logitudinal electroma-
gnetic elds and beam guides, J. Math. Phys., 48, 8 (2007) 082305-1, ..., 082305-15
[21] V.G. Bagrov, D.M. Gitman, I.M. Ternov et al.
Equations
Exact Solutions of the Relativistic Wave
(Nauka, Novosibirsk, 1982) pp. 1-144.
[22] V.G. Bagrov and D.M. Gitman,
Exact Solutions of Relativistic Wave Equations
pp. 1321
(Kluwer Acad. Publisher, Dordrecht Boston London, 1990).
[23] V.G. Bagrov, P.V. Bozrikov and D.M. Gitman, A charge in quantized plane-wave eld, Izw. VUZov
Radiozika (Sov. Journ. Radiophys.), XVI, I (1973) 129-140.
[24] V.G. Bagrov, P.V. Bozrikov and D.M. Gitman, An Electron in the quantized electromagnetic plane-
wave eld, Theor. Mat. Fiz., 14 2 (1973) 202-210.
[25] V.G. Bagrov, P.V. Bozrikov, D.M. Gitman and P.M. Lavrov, An Electron in a Field of a Plane
Quantized Monochromatic Electromagnetic Wave, Izw. VUZov Fizika 16 No. 8 (1973) 55-58; (Soviet
Physics Journal
16 No. 8 (1973) 1082-1085)
[26] V.G. Bagrov, D.M. Gitman, and V.A. Kuchin, Interaction with an external eld in quantum elec-
trodynamics, Izw. VUZov Fizika (Sov. Phys. Journ.) 4 (1974) 152-153.
[27] V.G. Bagrov, D.M. Gitman and P.M. Lavrov, Electron in a Quantized Field of a Plane Wave and
in a Classical Field of Redmond's Conguration, Izw. VUZov Fizika 17 No.6 (1974) 47-51; (Soviet
Physics Journal
17 No. 6 (1974) 787-790)
[28] V.G. Bagrov, D.M. Gitman and P.M. Lavrov, Electron in Constant Crossed Electromagnetic Fields
and Plane-Wave Fields, Izw. VUZov Fizika 17 NO.6 (1974) 68-74; (Soviet Physics Journal 17 No.6
(1974) 806-811)
[29] V.G. Bagrov, P.V. Bozrikov and D.M. Gitman, Fermion with Anomalous Moment in a Field of
Quantized Plane Wave, Izw. VUZov Fizika 17 No. 6 (1974) 129-132; (Soviet Physics Journal 17 No.
6(1974) 864-866)
20
[30] V.G. Bagrov, D.M. Gitman and V.A. Kuchin, Electron in the Field of Classical and a Quantized
Plane Wave traveling in the Same Direction, Izw. VUZov Fizika 17 No. 7 (1974) 60-64; (Soviet Physics
Journal
17 No. 7 (1974) 952-956)
[31] V.G. Bagrov, D.M. Gitman, V.A. Kuchin and P.M. Lavrov, Basises of electrodynamics of electrons
interacting with quantized plane wave eld. I, Izw. VUZov Fizika (Sov. Phys. Journ.) 12 (1974) 89-94.
[32] V.G. Bagrov, D.M. Gitman, V.A. Kuchin and P.M. Lavrov, Basises of electrodynamics of electrons,
interacting with quantized plane wave eld. II, Izw. VUZov Fizika (Sov. Phys. Journ.) 7 (1975) 11-15.
[33] V.G. Bagrov, D.M. Gitman and Sh.M. Shvartsman, Electron in a Quantized Plane Wave-Field and
the Classical Field of a Longitudinal Electric Wave, Izw. VUZov Fizika 18 No. 3 (1975) 67-71; (Soviet
Physics Journal
18 No. 3 (1975) 374-350)
[34] V.G. Bagrov, I.L. Buchbinder, D.M. Gitman and P.M. Lavrov, Coherent states of the electron in
quantized electromagnetic wave, Theor. Mat. Fiz. 33 (1977) 419-426.
[35] S.P. Gavrilov, D.M. Gitman and Sh. M. Shvartsman, Green's functions in external electric eld,
Sov. Journ. Nucl. Phys. (Yadern. Fizika)
29 (1979) 1097-1109
[36] S.P. Gavrilov, D. M. Gitman and Sh.M. Shvartsman, Green's functions in external electric eld and
its combination with magnetic eld and plane-wave eld, Sov. Journ. Nucl. Phys. (Yadern. Fizika),
29 (1979) 1392-1405.
[37] S.P. Gavrilov, D.M. Gitman and Sh.M. Shvartsman, Green's functions in external electric eld and
its combination with magnetic eld and plane-wave eld, Kratk. Soob. Fiz. (Lebedev Inst.), No. 2
(1979) 22-26.
[38] E.S. Fradkin and D.M. Gitman, Problems of quantum electrodynamics with intensive eld. (Appen-
dix), Preprint PhIAN (Lebedev Institute), 107 (1979) 1-40.
[39] V.G. Bagrov, V.P. Barashev, D.M. Gitman, and Sh.M. Shvartsman, Green functions in exter-
nal electromagnetic eld, in Collection Quantum processes in intense external elds, pp. 101-111,
(Shteentza, Kishenev, 1987) (3B348b88)
[40] D.M. Gitman, M.D. Noskov and Sh.M. Shvartsman, Green's functions in external electromagnetic
eld, Izw. VUZov Fizika (Sov. Phys. Journ.) 5 (1989) 59-64.
[41] D.M. Gitman, M.D. Noskov and Sh.M. Shvartsman, Quantum eects in a combination of a constant
uniform eld and a plane wave eld, Intern. Journ. Mod. Phys. A 6 (1991) 44374489.
[42] S.P.Gavrilov, D.M.Gitman, Green's Functions and Matrix Elements in Furry Picture for Electro-
weak Theory with non-Abelian External Field, Izw. VUZov Fizika (Russian Phys. Journ.) 36, No 5
(1993) 448-452.
[43] D.M. Gitman, Sh.M.Shvartsman and W.da Cruz, Path Integral over Velocities for Relativistic Par-
ticle Propagator, Bras. Journ. Phys. 24, No.4 (1994) 844-854.
[44] D.M. Gitman, S.I. Zlatev and W.da Cruz, Spin Factor and Spinor Structure of Dirac Propagator
in Constant Field, Bras. Journ. Phys. 26 (1996) 419-425
[45] D.M. Gitman and S.I. Zlatev, Spin factor in path integral representation for Dirac propagator in
external eld, Phys. Rev. D55 (1997) 7701-7714
[46] S.P. Gavrilov and D.M. Gitman, Proper time and path integral representations for the commutation
function, J. Math. Phys. 37 (7) (1996) 3118-3130
[47] D.M. Gitman and S.I. Zlatev, Semiclassical Form of the Relativistic Particle Propagator, Mod.
Phys. Lett.A
12 (1997) 2435-2443
[48] V.G. Bagrov, D.M. Gitman, and V.B. Tlyachev, The exact solutions of relativistic wave equations
for Aharonov-Bohm eld in combination with other electromagnetic elds, Proceedings of FORA, No.
6 (2001) 11-4
21
[49] V.G. Bagrov, D.M. Gitman, and V.B. Tlyachev, Solutions of relativistic wave equations in super-
positions of Aharonov-Bohm, magnetic, and electric elds, J. Math. Phys. 42, No.5 (2001)
[50] V.G. Bagrov, M.C. Baldiotti, D.M. Gitman, and I.V. Shirokov, New solutions of relativistic wave
equations in magnetic eld and longitudinal elds, J.Math. Phys. 43 (2002) 2284-2295
[51] S.P. Gavrilov, D.M. Gitman, and A.A. Smirnov, Dirac equation in the magnetic-solenoid eld,
Europ. Phys. Journ. C
30 (2003) 009
[52] S.P. Gavrilov, D.M. Gitman, and A.A. Smirnov, Green functions of the Dirac equation with
magnetic-solenoid eld, J. Math. Phys. 45 (2004) 1873
[53] S.P. Gavrilov, D.M. Gitman, and A.A. Smirnov, Self-adjoint extensions of Dirac Hamiltonian in
magnetic-solenoid eld and related exact solutions, Phys. Rev. A 67 (2003) 024103(4)
[54] S.P. Gavrilov, D.M. Gitman, A.A. Smirnov, and B.L. Voronov, Dirac fermions in a magnetic-
solenoid eld, Focus on Mathematical Physics Research Ed. by Charles V. Benton (Nova Science
Publishers, New York, 2004) pp. 131-168, ISBN:1-59033-923-1
[55] V.G. Bagrov, D.M. Gitman, A. Levin, and V.B. Tlyachev, Aharonov-Bohm Eect in cyclotron and
synchrotron radiations, Publicação IFUSP 1395/2000; hep-th/0001108; quant-ph/001022, Nucl. Phys.
B605 (2001) 425-454
[56] V.G. Bagrov, D.M. Gitman, A. Levin, and V.B. Tlyachev, Impact of Aharonov-Bohm Solenoid on
Particle Radiation in Magnetic Field, Mod.Phys.Lett. A16, No. 18 (2001) 1171-1179
[57] V.G. Bagrov, D.M. Gitman, and V.B. Tlyachev, l-dependence of particle radiation in magnetic-
solenoid eld and Aharonov-Bohm Eect, Int. Journ. Mod. Phys. A17 (2002) 1045-1048
[58] V.G. Bagrov, D.M. Gitman, and V.B. Tlyachev, Aharonov-Bohm Eect in Synchrotron Radiation,
Proceedings of FORA, No. 5 (2000) 7-26
[59] V.G. Bagrov, V.G. Bulenok, D.M. Gitman, V.B. Tlyachev, J.A. Jara, and A.T. Jarovoi, Angular
behavior of synchrotron radiation harmonics, Phys. Rev. E 69, 046502 (2004)
[60] V.G. Bagrov, V.G. Bulenok, D.M. Gitman, V.B. Tlyachev, and A.T. Jarovoi, New results in clas-
sical theory of synchrotron radiation, Surface. Roentgen, synchrotron, and neutron studies. No. 11
(2003) pp. 59-65.
[61] V.G. Bagrov, D.M. Gitman, V.B. Tlyachev, and A.T. Jarovoi, Evolution of angular distribution of
polarization components of synchrotron radiation under changes of particle energy, Recent Problems
in Field Theory, Proceedings of XV International Summer School
Volga 22.June-03. July 2003,
Kazan, Russia, (Kazan, 2004) pp. 9-23
[62] V.G. Bagrov, D.M. Gitman, V.B. Tlyachev, and A.T. Jarovoi, Evolution of angular distribution of
polarization components for synchrotron radiation under changes of particle energy, Proceedings of
the Eleventh Lomonosov Conference on Elementary Particle Physics Particle Physics in Laboratory,
Space and Universe, 21-27 August 2003, Moscow, Russia (World Scientic, New Jersey, Singapore
2005)
[63] V.G. Bagrov, D.M. Gitman, V.B. Tlyachev, A.T. Jarovoi, New theoretical Results in Synchrotron
Radiation, Nuclear Instruments & Methods in Physics Research, B240 (2005) pp 638 - 645
[64] B.L. Voronov, D.M. Gitman, and I.V. Tyutin, Constructing quantum observables and self-adjoint
extensions of symmetric operators I, Russian Phys. Journ. No. 1 (2007) 1-31
[65] B.L. Voronov, D.M. Gitman, and I.V. Tyutin, Constructing Quantum Observables and Self-Adjoint
Extensions of Symmetric Operators II. Dierential Operators, Russian Physics Journ. 50 No. 9 (2007)
853-884
22
[66] B.L. Voronov, D.M. Gitman, and I.V. Tyutin, Constructing quantum observables and self-adjoint
extensions of symmetric operators III. Self-adjoint boundary conditions, Izv. Vuzov Fizika, 51, No. 2
(2008) 3-43 (in Russian); Russian Phys. Journ.
51, No. 2 (2008) 115-157 (English translation)
[67] B.L. Voronov, D.M. Gitman, and I.V. Tyutin, The Dirac Hamiltonian with a superstrong Coulomb
eld, Theoretical and Mathematical Physics, 150(1) (2007) 34-72
[68] D.M. Gitman, A. Smirnov, I.V. Tyutin, and B.L. Voronov, Self-adjoint Schrödinger and Dirac
operators with Aharonov-Bohm and magnetic-solenoid elds, arXiv:0911.0946v1 [quant-ph]
[69] D.M. Gitman, I.V. Tyutin, and B.L. Voronov, Self-adjoint extensions and spectral analysis in
Calogero problem, J. Phys. A43 (2010) 145205 (34pp)
[70] D.M. Gitman, I.V. Tyutin, and B.L. Voronov, Oscillator representations for self-adjoint Calogero
Hamiltonians, arXiv:0907.1736v1 [quant-ph]
10.4
Integrais de trajetória; teoria de grupos em mecânica quântica relativística e
teoria de campos; métodos semiclássicos e estados coerentes
•
A abordagem da integral de trajetória foi usada na QED com vácuo instável para calcular a
matriz densidade de partículas criadas por campos externos [1, 2].
Uma integral de trajetória
foi construída, pela primeira vez, apresentando o funcional gerador com duas fontes, que aparece
sempre na teoria quântica de campos com vácuo instável [3, 4, 5].
•
A generalização da conhecida abordagem de integral de trajetória na teoria de perturbação para
o caso da presença de graus de liberdade Grassmanianos (super-generalização) foi elaborada em
detalhes e estendida ao caso das teorias com vínculos [6, 7].
•
Foram construídos diferentes tipos de representações de propagadores de partículas relativísticas
por integral de trajetória [25, 26, 30, 31, 2, 30, 14, 34, 13, 36]. Podem-se mencionar aqui duas
super-generalizações da representação de tempo próprio de Schwinger, introduzidas pela primeira
vez.
Foi mostrado pela primeira vez que podem ser feitas todas as integrações de Grassman
nas representações por integral de trajetória para propagadores de partículas com spin, assim
como foram obtidas expressões para o chamado fator espinorial em campos arbitrários externos
[27, 30, 45].
Usando as representações por integral de trajetória obtidas, foram calculados os
propagadores de partículas em várias congurações de campos externos [30, 31, 4, 44, 45].
•
Uma aplicação das integrais de trajetória de Grassmann ao cálculo de operadores foi desenvolvida
no trabalho [35].
•
Nos artigos [14, 15, 16, 17, 18, 19, 20], foram estudados estados coerentes de grupos de Lie e suas
aplicações. Por exemplo, foi dada uma construção para todos os grupos
SU (N )
e
SU (l + 1).
Referências
[1] I.L. Buchbinder, D.M. Gitman and V.P. Frolov, Density matrix for particle-creation processes in
external eld, Izw. VUZov Fizika (Sov. Phys. Journ. 529-533) 6 (1980) 77-81.
[2] V.P. Barashev, E.S. Fradkin, D.M. Gitman and Sh.M. Shvartsman, The problems of QED with
unstable vacuum. Reduction formulas. The density matrix of particles creating in an external eld,
201 (1990) 74-94.
[3] I.L. Buchbinder, E.S. Fradkin and D.M. Gitman, Generating functional in quantum eld theory with
unstable vacuum, Preprint PhIAN (Lebedev Institute), 138 (1981).
[4] D.M. Gitman and V.A. Kuchin, Generating functional of mean eld in quantum electrodynamics
with unstable vacuum, Izw. VUZov Fizika (Sov. Phys. Journ.) 10 (1981) 80-84.
23
presence of an external eld, violating the vacuum stability, Sov. Journal Nucl. Phys. (Yadernaja
Fizika),
46 (1987) 172-180.
Canonical quantization of elds with constraints
(Nauka,
Moscow, 1986) pp. 1-216.
Quantization of Fields with Constraints
pp. 1291 (Springer-
Verlag, Berlin Heidelberg New-York London Paris Hong-Kong Barcelona, 1990).
[8] V.G. Bagrov, D.M. Gitman and I.L. Buchbinder, Coherent states of relativistic particles, Izw. VUZov
8 (1975) 134-135.
[9] V.G. Bagrov, D.M. Gitman and V.A. Kuchin, Eigenfunctions of linear combinations of creation and
annihilation operators, Izw. VUZov Fizika (Sov. Phys. Journ.) 9 (1975) 13-19.
[10] V.G. Bagrov, D.M. Gitman and V.A. Kuchin, External eld in quantum electrodynamics and co-
herent states In Actual problems of theoretical physics (Moscow State University, Moscow, 1976) pp.
334-342.
[11] V.G. Bagrov, I.L. Buchbinder and D.M. Gitman, Coherent states of a relativistic particle in an
external electromagnetic eld, Journ. Phys. A 9 (1976) 1955-1965.
[12] V.G. Bagrov, I.L. Buchbinder, D.M. Gitman and P.M. Lavrov, Coherent states of the electron in
quantized electromagnetic wave, Theor. Mat. Fiz. 33 (1977) 419-426.
[13] V.G. Bagrov, I.L. Buchbinder and D.M. Gitman, Construction of coherent states for relativistic
particles in external elds, In Group Theoretical Methods in Physics Proceedings of First Zvenigorod
Seminar, (Nauka, Moskva, 1980) pp. 232-239.
[14] D.M. Gitman and A.L. Shelepin, Coherent states related to groups
SU (N )
and
SU (N, 1),
Izw.
1 (1990) 8389.
[15] D.M. Gitman, S.M. Carchev and A.L. Shelepin, Coherent states for groups
SU (N )
and
SU (N, 1)
and its applications in relativistic quantum theory, Trudy PhIAN (Proceedings of Lebedev Institute,
Moscow),
201 (1990) 95-138.
[16] D.M. Gitman and A.L. Shelepin, Coherent states for variables angular momentum-angle, Kratk.
Soob. Fiz. (Lebedev Inst.)
1 (1990) 31-33.
[17] D.M. Gitman and A.L. Shelepin, Coherent states of the
SU (N )
and
SU (N, 1)
groups and quanti-
zation on the corresponding homogeneous spaces, Preprint MIT, CTP # 1990 (1991) 1-32.
[18] D.M. Gitman and A.L. Shelepin, Coherent States of the
SU (N )
and
SU (N, 1)
groups, in Proc.
XVIII International Colloquium on Group Theoretical Methods in Physics, Moscow, June 1990
(Springer-Verlag, 1990).
[19] D.M. Gitman and A.L. Shelepin, Coherent States of the
SU (N )
groups, Journ. Phys. A 26 (1993)
313-327.
[20] D.M.Gitman, A.L.Shelepin, Coherent States of SU(l,1) Groups, Journ. Phys. A
26 (1993) 7003-
7018.
[21] J.P. Gazeau, M.C. Baldiotti, and D.M. Gitman, Coherent states of a particle in magnetic eld and
Stieltjes moment problem, Physics Letters A 373 (2009) 1916-1920
[22] D.M. Gitman and A.L. Shelepin, Representations of SU(N) groups on the polunomials of the anti-
commuting variables, Kratk. Soob. Fiz. (Lebedev Institute) No.11 (1998) pp.21-30
[23] V.G. Bagrov, D.M. Gitman and V.D. Skarginski, Aharonov-Bohm eect for quantum states of
relativistic electron in homogeneous magnetic eld and in thin solenoid eld, Preprint PhIAN (Lebedev
Institute),
101 (1986) 1-18.
24
[24] V.G. Bagrov, D.M. Gitman and V.D. Skarginski, Aharonov-Bohm eect for stationary and coherent
states of an electron in homogeneous magnetic eld, Trudy PhIAN (Proceedings of Lebedev Institute,
Moscow),
176 (1986) 151-166.
[25] E.S. Fradkin, D.M. Gitman and Sh.M. Shvartsman, Path integral for relativistic particle theory,
Europhys. Lett.
15 (3) (1991) 241-244.
[26] E.S. Fradkin and D.M. Gitman Path integral representation for the relativistic particle propagators
and BFV quantization, Phys. Rev. D 44 (1991) 3230-3236.
[27] D.M. Gitman, Sh.M.Shvartsman, Spinor and isospinor structure of relativistic particle propagator,
Preprint IC/93/197, pp.1-8; hep-th/9310142; Phys. Lett.
B
B 318 (1993) 122-126; Errata, Phys. Lett.
331 (1994) 449,450
[29] D.M. Gitman, S.I. Zlatev and W.da Cruz, Spin Factor and Spinor Structure of Dirac Propagator
in Constant Field, Bras. Journ. Phys. 26 (1996) 419-425
[30] D.M. Gitman, Pseudoclassical Theory of Relativistic Spinning Particle, Preprint IFUSP/P-1173,
pp.1-27, September/1995, in Topics in Statistical and Theoretical Physics, F.A. Berezin Memorial
vol. American Mathematical Society Translation, Series 2, vol. 177, pp. 83-104, Amer. Math. Soc.,
Providence, RI, 1996
[31] D.M. Gitman and S.I. Zlatev, Spin factor in path integral representation for Dirac propagator in
external eld, Phys. Rev. D55 (1997) 7701-7714
[32] S.P. Gavrilov and D.M. Gitman, Proper time and path integral representations for the commutation
function, J. Math. Phys. 37 (7) (1996) 3118-3130
[33] D.M. Gitman, Path integrals and pseudoclassical description for spinning particles in arbitrary
dimensions, Nucl. Phys. B 488 (1997) 490-512
dimensions, in Functional Integration: Basics and Applications, Ed. C. DeWitt-Morette, P. Cartier,
and A. Folacci, NATO ASI Series B: Physics Vol.361, p 418, (Plenum Publishing Corp. 1997)
[35] D.M. Gitman, S.I. Zlatev and P.B. Barros, Application of Path Integration to Operator Calculus,
J. Phys. A: Math.Gen.
31 (1998) 7791-7799
[36] D.M. Gitman and S.I. Zlatev, Semiclassical Form of the Relativistic Particle Propagator, Mod.
Phys. Lett.A
12 (1997) 2435-2443
[37] V.G. Bagrov, S.P. Gavrilov, D.M. Gitman, and D. P. Meira Filho, Coherent states of spinless
particle in large magnetic-solenoid eld, Problems of Modern Theoretical Physics (A volume
in honour of Professor I.L. Buchbinder in the occasion of his 60th birthday) (Tomsk State University
Press, Toms 2008) pp 57-77; ISBN 978-5-89428-280-0
[38] V.G. Bagrov, S.P. Gavrilov, D.M. Gitman, and D. P. Meira Filho, Coherent states of non-relativistic
electron in magneticsolenoid eld, e-Print: arXiv:1002.2256 [quant-ph], submitted to Journ. Physics.
A
[39] V.G. Bagrov, S.P. Gavrilov, D.M. Gitman, and D. P. Meira Filho, Coherent states of relativistic
electron in magneticsolenoid eld, to be published
25
10.5
Modelos clássicos e pseudoclássicos de partículas relativísticas e sua quantização
•
Foi apresentada uma generalização da ação pseudoclásssica de uma partícula com spin na presença
de um momento magnético anômalo [1, 2].
•
Foram propostos novos modelos pseudoclássicos para partículas relativísticas: para uma partícula
de Weyl [3]; para partículas com spin em 2+1 dimensões [6, 25, 26]; para a partícula de Weyl em
10 dimensões [7, 8, 18, 19]; para partículas massivas com spin 1 (partículas de Chern-Simons) [9]
e para partículas massivas com spins altos (inteiros e semi-inteiros) em 2+1 dimensões [10, 11]
(ambos modelos supersimétricos); para partículas massivas de Dirac (spin 1/2) em dimensões
ímpares arbitrárias [12, 13].
•
Foi considerado um procedimento consistente de quantização canônica de modelos pseudoclássicos
de partículas relativísticas com spin 1. A mecânica quântica construída para o caso massivo prova
ser equivalente à teoria de Proca e, para o caso sem massa, à teoria de Maxwell [5].
•
O propagador de uma partícula espinorial em campos abelianos externos e em dimensões arbitrárias foi apresentado por meio de uma integral de trajetória [14].
•
Foi construida uma representação por integral de trajetória para a função de comutação do campo
espinorial quantizado interagindo com campos eletromagnéticos externos arbitrários [46].
•
Foi feita, pela primeira vez, a quantização canônica de partículas relativísticas com spin 0, 1/2 e 1
através de um novo gauge temporal proposto [15, 16, 17], e foi construída,pela primeira vez, uma
mecânica quântica relativística consistente.
•
Outros trabalhos relevantes nesta área foram [27, 28, 29].
Referências
[1] D.M.Gitman, A.V.Saa, Pseudoclassical Model of Spinning Particle with Anomalous Magnetic Mo-
mentum, Mod. Phys. Lett. A, 8 (1993) 463-468.
[2] D.M.Gitman, A.V.Saa, Quantization of Spinning Particle with Anomalous Magnetic Momentum,
Class. Quantum Grav.
10 (1993) 1447-1460.
[3] D.M. Gitman, A.E. Gonçalves and I.V. Tyutin, New pseudoclassical model for Weyl particles, Phys.
Rev. D
50 (1994) 5439-5442.
[5] D.M. Gitman, A.E. Gonçalves and I.V. Tyutin, Quantization of a pseudoclassical model of the spin
1 relativistic particle, Int.J.Mod.Phys. A 10 (1995) 701-718.
[6] D.M. Gitman, A.E. Gonçalves and I.V. Tyutin, Pseudoclassical Supergauge Model for 2+1 Dirac
Particle, Physics of Atomic Nuclei, 60 No.4 (1997) 748-752
[7] D.M. Gitman and A.E. Gonçalves, Pseudoclassical model for Weyl particle in 10 dimensions, J.
Math. Phys.
38 (5) (1997) 2167-2170
[8] D.M. Gitman, Pseudoclassical Theory of Relativistic Spinning Particle, in Topics in Statistical and
Theoretical Physics, F.A. Berezin Memorial vol. American Mathematical Society Translation, Series
2, vol. 177, pp. 83-104, Amer. Math. Soc., Providence, RI, 1996
[9] D.M. Gitman and Tyutin, Pseudoclassical model for Chern-Simons particles, Mod. Phys. Lett. A11
(1996) 381-388
[10] D.M. Gitman and Tyutin, Pseudoclassical description of higher spins in 2+1 dimensions, Int.
J.Mod.Phys.A
12 (1997) 535-556
26
[11] D.M. Gitman and I.V. Tyutin, Pseudoclassical description of higher spins in 2+1 dimensions, in
Proceedings of SECOND INTERNATIONAL SAKHAROV CONFERENCE ON PHYSICS, Moscow,
Russia, 20-24 May 1996, ed. I.M. Dremin, A.M. Semikhatov, (World Sci. Singapore, 1997) 428-434
[12] D.M. Gitman and A.E. Gonçalves, Pseudoclassical description of the massive Dirac particles in odd
dimensions, Int. J. Theor.Phys. 35 (1996) 2427-2438
[13] D.M. Gitman, Quantization of Spinning Particles in Odd Dimensions, Nucl. Phys. B (Proc. Suppl.)
57 (1997) 231-234
dimensions, Nucl. Phys. B 488 (1997) 490-512
[15] D.M. Gitman and I.V. Tyutin, Canonical quantization of the relativistic particle, JETP Lett.
v. 4 (1990) 214; Pis'ma Zh. Eksp. Teor. Fiz.
51,
51, v. 3 (1990) 188190.
[16] D.M. Gitman and I.V. Tyutin, Classical and quantum mechanics of the relativistic particle, Class.
and Quantum Grav.
7 (1990) 2131-2144.
[17] G. Fulop, D.M. Gitman and I.V. Tyutin, Reparametrization Invariace as Gauge Symmetry, Preprint
IFUSP/P-1263, pp.1-30, April/1997; hep-th/9805040; Int. J. Theor. Phys.
38 (1999) 1953-1980
[18] D.M. Gitman, A.E. Gonçalves and I.V. Tyutin, Remark to the Comment on New pseudoclassical
model for Weyl particles, Preprint FIAN/TD/96-03; hep-th/9602151
[19] D. M. Gitman, and I.V. Tyutin, A pseudo-classical model of a Weyl particles and quantization of
classical constants, Russian Physics Journal 45, No.7 (2002) pp. 690-694
[20] A.A. Deriglazov and D.M. Gitman, Classical description of spinning degrees of freedom of relativistic
particles by means of commuting spinors, Publicação IFUSP 1324/98; hep-th/9811229; Mod. Phys.
Lett.
A14 (1999) pp. 709-720
[21] S.P. Gavrilov, D.M. Gitman, Quantization of Point-Like Particles and Consisitent Relativistic
Quantum Mechanics, Int. J. Mod. Phys. A15 (2000) 4499-4538
[22] S.P. Gavrilov, D.M. Gitman, Quantization of the Relativistic Particle, Class.Quant.Grav.
17 issue
19 (2000) L133-L139
[23] S.P. Gavrilov, D.M. Gitman, Quantization of the Relativistic Particle and Consistent Relativistic
Quantum Mechanics, Proceedings of the International Conference Quantization, gauge theories, and
strings, Moscow, Russia, June 5-10, 2000 dedicated to the memory of Professor Em Fradkin, Ed.
A. Semikhatov, M. Vasiliev, V. Zaikin, v.II (Scientic World, 2001) pp.27-35.
[24] S.P. Gavrilov, D.M. Gitman, Quantization of a spinning particle in an arbitrary background,
Class.Quant.Grav.
18 (2001) 2989-2998
[25] R. Fresneda, S. Gavrilov, D. Gitman, and P. Moshin, Quantization of ( 2
+ 1)-spinning
particles
and bifermionic constraint problem, Class.Quant.Grav.21 (2004) pp.1419-1442
[26] S.P. Gavrilov, D.M. Gitman, and J.L. Tomazelli, Comments on spin operators and spin-polarization
states of
2+1
fermions, Eur. Phys. J. C (2005) DOI: 10.1140/epjc/s2004-02026-9
[27] D.M. Gitman, Berezin-Marinov's pseudoclassical action, Reminiscences
about Felix Berezin-
founder of supermathematics, ed. by E. Karpel, P.A. Minlos, I.V. Tyutin, and D.A. Leites, and
(M(TZ)NMO, Moscow 2009) pp. 139-148; ISBN 978-5-94057-458-3
[28] R. Fresneda and D. Gitman, Pseudoclassical description of scalar particle in non-Abelian background
and path-integral representations, Intern. Journ. Mod. Phys. A 23 (6) (2008) 835-853.
[29] D. Gitman and V.G. Kupriyanov, Path integral representations in noncommutative quantum me-
chanics and noncommutative version of Berezin-Marinov action, Europ. Phys. J. C 54 (2008) 325-332
27
10.6
•
Teoria dos spins altos
Foi realizada uma abordagem geral da descrição dos spins altos na qual um campo escalar sob
o grupo de Poicaré é considerado como uma função geradora para campos multicomponentes
convencionais. Essa abordagem fornece uma consideração unicada para o problema da construção
de equações de onda relativísticas de diferentes tipos e justica o uso de métodos da teoria de
grupos [1, 2, 3, 10, 13, 14, 15].
•
Foi proposta uma descrição mecânico quântica de objetos relativísticos orientáveis. Ela gereraliza
as idéias de Wigner relativas ao tratamento de objetos não relativísticos orientáveis (em particular,
um rotador não relativístico) ,com o auxílio de dois referenciais (um xo no espaço e outro xo
no corpo) [16, 17].
•
Outros trabalhos relevantes: [3, 4, 5, 6, 7, 8, 9, 11, 12].
Referências
[1] D.M.Gitman, A.L.Shelepin, 2+1 Poincare group and relativistic wave equations, Proceedings of VII
International Conference on Symmetry Methods in Physics, Dubna, July 1995, v1, pp.212-219, (JINR,
Dubna 1996).
[2] D.M.Gitman, A.L.Shelepin, Poincare group and relativistic wave equations in 2+1 dimensions, J.
Phys. A: Math. Gen.
30 (1997) 6093-6121
[3] D.M. Gitman and I.V. Tyutin, Pseudoclassical description of higher spins in 2+1 dimensions, in
Proceedings of SECOND INTERNATIONAL SAKHAROV CONFERENCE ON PHYSICS, Moscow,
Russia, 20-24 May 1996, ed. I.M. Dremin, A.M. Semikhatov, (World Sci. Singapore, 1997) 428-434
[4] A.V. Galajinsky and D.M. Gitman, Siegel superparticle, higher order fermionic constraints, and path
integrals, hep-th/9805044, Preprint IFUSP/P-1308, pp.1-22, Maio/1998; Nucl. Phys. B536 (1999)
435-453
[5] A.A. Deriglazov and D.M. Gitman, The Gree-Schwarz type formulation of D=11 S-invariant super-
string and superparticle action, Preprint IFUSP/P-1304, pp.1-30, Abril/1998; hep-th/9804055, Int.
J. Mod. Phys.
A14, No.17 (1999) 2769-2790
[6] A.A. Deriglazov, Galajinsky, and D.M. Gitman, On zero modes of the eleven dimensional superstring,
Preprint IFUSP/P-1298, pp.1-7, Março/1998; hep-th/9801176; Phys. Rev.
D59 (1999) 048902(4)
[7] A.A. Deriglazov, A.V. Galajinsky, and D.M. Gitman, Massless chiral multiplet model as rst quan-
tized ABsuperparticle, Proceedings of Second International Conference Quantum Field theory and
Gravity (July 28August 2, 1997, Tomsk), Tomsk, Russian Federation 1998, pp. 164172, Eds. I.
Buchbinder and K. Osetrin
[8] A.A. Deriglazov and D.M. Gitman, Examples of D=11 S-supersymmetric Actions for Point-Like
Dynamical Systems, Mod. Phys. Lett. A13 (1998) 2559-2570
[9] A.V. Galajinsky and D.M. Gitman, On minimal coupling of the ABC-superparticle to supergravity
background, Phys. Rev. D59 (1999) 047504
[10] D.M. Gitman, and A. Shelepin, Fields on the Poincaré Group:
Arbitrary spin description and
relativistic wave equations, Int.J.Theor.Phys. 40 (2001) 603-684
[11] I.L. Buchbinder, D.M. Gitman, V.A. Krykhtin, and V.D. Pershin, Equations of motion for massive
spin 2 eld coupled to gravity, Nucl.Phys. B584 No.1-2 (2000) 615-640
[12] I.L. Buchbinder, D.M. Gitman, and V.D. Pershin, Causality of Massive Spin 2 Field in External
Gravity,Phys.Lett.B492 (2000) 161-170
28
[13] D.M. Gitman, and A. Shelepin, Z-description of the relativistic spin, Proceedings of XXIII International Colloquium on Group Theoretical Methods in Physics, Edited by A.N.Sissakian, G.S.Pogosyan
and L.G.Mardoyan, V.2 (Dubna, JINR, 2002) pp.376-384
[14] I.L. Buchbinder, D.M. Gitman, and A.L. Shelepin, Discrete symmetry transformations as automor-
phisms of the proper Poincare group, Int. J. Theor. Phys. 41, No. 4 (2002) 753-790
[15] D.M. Gitman, and A. Shelepin, Z-description of the relativistic spin, Hadronic Physics, No. 3,4
(Special Issue on HIGHER SPINS, QCD, AND BEYOND ) (2003) pp.259-274
[16] D.M. Gitman and A. Shelepin, Field on Poincaré Group and Quantum Description of Orientable
Objects, Europ. Physical Journal C, 61, Issue1 (2009)111
[17] D.M.
Gitman
and
A.L.
Shelepin,
Classication
of
quantum
relativistic
orientable
objects,
arXiv:1001.5290v1 [hep-th], submitted to Class. Quantum Grav.
10.7
Teoria de sistemas de dois e quatro níveis e aplicações à computação quântica
•
Foi apresentado um estudo detalhado da equação de spin, ou seja, o sistema de dois níveis descrito
por duas equações diferenciais acopladas dependentes do tempo. Foram obtidas 26 novas classes
de soluções exatas para tais sistemas [1, 3, 4, 5].
•
Foi desenvolvido um método sistemático para a obtenção de novas soluções da equação de spin
a partir de uma solução previamente conhecida, utilizando uma adaptação do método da transformação de Darboux para a equação diferencial que descreve um sistema de dois níveis.
Foi
demonstrada a existência de transformações sob as quais a forma das equações dos sistemas de
dois níveis é invariante. Em especial, foi construído um operador de Darboux que transforma o
problema dado por campos reais em um novo problema também dado por campos reais [2, 3].
•
Foi desenvolvido um estudo detalhado da equação de dois spins acoplados (sistemas de quatro
níveis) e, em especial, foi demonstrado como é possível construir soluções exatas deste problema
a partir de soluções conhecidas do sistema de dois níveis [6].
•
Foi desenvolvido um método para a obtenção de soluções exatas da equação de spin para o caso
importante de campos externos cuja atuação efetiva esteja restrita a um intervalo de tempo nito
[8].
•
Utilizando as soluções exatas dos sistemas de dois e quatro níveis, foi descrita a implementação
teórica de um conjunto de portas lógicas quânticas universais,estudando, em especial, as características dos campos externos e os possíveis cenários práticos para a implementação destes dispositivos
[7, 9].
Referências
[1] V.G. Bagrov, J.C.A. Barata, D.M. Gitman, and W.F. Wreszinski, Aspects of Two-Level Systems
under External Time Dependent Fields , J. Phys. A34 (2001) 10869-10879
[2] V.G. Bagrov, M.C. Baldiotti, D.M. Gitman, and V.V. Shamshutdinova, Darboux transformation for
two-level system, Annalen der Physik 14 (2005) 390-397
[3] V.G. Bagrov, M.C. Baldiotti, D.M. Gitman, and A.D. Levin, Spin equation and its solutions, Annalen
der Physik
14 [11-12] (2005) pp.764-789
[4] D.M. Gitman, B.F. Samsonov, V.V. Shamshutdinova, Polynomial pseudosupersymmetry underlying
a two-level atom in an external electromagnetic eld, Czech. J. Phys. 55, No.9 (2005) pp. 1173-1176
[5] B.F. Samsonov, V.V. Shamshutdinova, D.M. Gitman, Two-level systems: exact solutions and un-
derlying pseudo-supersymmetry, Ann. Phys. N.Y. 322 (2007) 1043-1061
29
[6] V.G. Bagrov, M.C. Baldiotti, D.M. Gitman, and A.D. Levin, Two interacting spins in external eld.
Four-level systems, Annalen der Physik, 16, 8 (2007) 274-285
[7] M.C. Baldiotti, D.M. Gitman, Four-level systems and a universal quantum gate, Annalen der Physik
(Berlin) 17, pp. 450-459 (2008)
[8] V.G. Bagrov, M.C. Baldiotti, D.M. Gitman, and A.D. Levin, Two and four-level systems in magnetic
elds restricted in time, Publicação IFUSP ; e-Print: arXiv:0803.0299, submitted to Annalen der
Physik
[9] M.C. Baldiotti, V.G. Bagrov, and D.M. Gitman, Two Interacting Spins in External Fields and
Application to Quantum Computation, Physics of Particles and Nuclei Letters, 6, No. 7 (2009) pp.
559-562
10.8
•
Mecânica quântica e teoria de campos nos espaços não comutativos
Foi introduzido um plano de Moyal, cujo parâmetro da não comutatividade das coordenadas
θµν
é construído por dois parâmetros bifermiônicos (elementos que compõem uma álgebra de
Grassmann).
Neste tratamento, o produto de Moyal contém um número nito de derivadas, o
que permite evitar diculdades em comparação com o procedimento padrão. Foram analisadas as
propriedades de renormalizabilidade de teorias não comutativas deste tipo [1, 3].
•
Foi discutida a construção de ações (pseudo) clássicas
θ-modicadas
(modicadas pela não comu-
tatividade das coordenadas) para as partículas relativísticas escalar e espinorial. Foi considerada
a dinâmica clássica e quântica de uma partícula caregada em espaços não comutativos [2, 4, 5].
•
Foi analisada a modicação dos níveis de energia do átomo de hidrogênio relativístico devida à
não comutatividade do espaço. Foi construída a
a interação
θ-modicada
θ-modicação
θ-modicação
da equação de Pauli. Foi extraída
entre o spin não relativístico e o campo magnético e foi construída uma
do modelo de Heisenberg para spins acoplados [6, 7].
Referências
[1] D. M. Gitman, D. V. Vassilevich, Space-time noncommutativity with a bifermionic parameter, Mod.
Phys. Lett.
23 (12) (2008) 887-893
[2] D. Gitman and V.G. Kupriyanov, Path integral representations in noncommutative quantum mecha-
nics and noncommutative version of Berezin-Marinov action, Europ. Phys. J. C 54 (2008) 325-332
[3] R. Fresneda, D.M. Gitman, and D.V. Vassilevich, Nilpotent noncommutativity and renormalization,
Phys. Rev. D78:
025004 (2008)
[4] D.M. Gitman and V.G. Kupriyanov, Gauge Invariance and Classical Dynamics of Noncommtative
Particle Theory, Journal of Mathematical Physics, 51, 022905 (2010) 022905 (1-8)
[5] J.P. Gazeau, M.C. Baldiotti, and D.M. Gitman, Semiclassical and quantum motion on non-
commutative plane, Physics Letters A, DOI information: 10.1016/j.physleta.2009.08.059
[6] T.C. Adorno, M.C. Baldiotti, M. Chaichian, D.M. Gitman, and A. Tureanu, Dirac Equation in
Noncommutative Space for Hydrogen Atom, Phys. Letters B 682, Issue 2, (2009) 235-239
[7] T.C. Adorno, M.C. Baldiotti, and D.M. Gitman, Quantum and pseudoclassical description of non-
relativistic spinning particles in noncommutative space, submitted to Physics Lett. B
10.9
Estatística quântica
De 1966 a 1970, trabalhou na área de Estatística Quântica, resolvendo os seguintes problemas:
•
Foram propostos novos tipos de equações integrais-diferenciais para funções de distribuição em
estatística clássica e quântica [1, 3, 5]
30
•
Foi proposta uma forma nova para a função de distribuição do tipo Wigner,para um sistema
quântico em equilíbrio térmico. Com base nessa representação,foram calculadas correções para a
distribuição clássica [2].
•
Nos artigos [4, 5, 6, 7, 8] foram estudados princípios variacionais em estatística quântica.
Em
particular, foi construído um princípio variacional para o potencial termodinâmico. Na verdade,
este foi um dos primeiros trabalhos, no qual a ideia de ação efetiva foi introduzida, e no qual, em
particular, foi demonstrado em detalhes o caso da estatística quântica.
Referências
[1] E.A. Arinshtein and D.M. Gitman, System of integral equations for partial distribution functions,
9 (1967) 110-113.
[2] E.A. Arinshtein and D.M. Gitman, Temperature dependence of quantum distribution functions, Izw.
9 (1967) 113-120.
[3] E.A. Arinshtein and D.M. Gitman, Integral equations for partial density matrices, Izw. VUZov Fizika
(Sov. Phys. Journ.)
8 (1968) 81-86.
[4] E.A. Arinshtein and D.M. Gitman, A variational principle for mean occupation numbers, Izw. VUZov
10 (1968) 146-147.
[5] D.M. Gitman, A system of integral equations for partial density matrices, Izw. VUZov Fizika (Sov.
Phys. Journ.)
12 (1969) 155-158.
[6] D.M. Gitman, An expression for the thermodynamical potential in the form of a stationary functional
on mean occupation numbers, Izw. VUZov Fizika (Sov. Phys. Journ.) 4 (1970) 96-102.
[7] D.M. Gitman and A.G. Tchernishov, A variational principle for the thermodynamical potential of a
two-component system Izw. VUZov Fizika (Sov. Phys. Journ.) 3 (1971) 30-35
[8] E.A. Arinshtein and D.M. Gitman, Equations for generating functional in classical and quantum
mechanics, Izw. VUZov Fizika (Sov. Phys. Journ.) 9 (1971) 98-102.
10.10
Outros assuntos
Referências
[1] D. Gitman, My Encounters with Felix Alexandrovich Berezin: Snapshots of Our Life in the 1960s,
'70s and Beyond, in FELIX BEREZIN. Life and Death of the Mastermind of Superma-
thematics, ed. by M. Shifman (World Scientic, Singapore 2007) pp 181-205; russian translation in
Reminiscences
about Felix Berezin-founder of supermathematics, ed. by E. Karpel, P.A.
Minlos, I.V. Tyutin, and D.A. Leites, and (M(TZ)NMO, Moscow 2009) pp. 282-301
[2] D.M. Gitman, I.V. Tyutin,J.L. Assirati, and M.G. da Costa, Structure of Lorentz transformation of
general form, Gravitation and Cosmology 4 No.2(14) (1998) 163-166
[3] E.R. Berdichevkaja, S.P. Gavrilov and D.M. Gitman, A mathematical model for calculation of the
trac capacity of machinery for production of integral schemes, Elektronaja Technika, 7 1 (1979)
83-90.
[4] D.M. Gitman, Quantization, pp. 311-312; Constraint, General, p. 112; Dirac Quantization Rules, pp.
129-130; Constraint Gauge Theories, pp. 109-112,
CONCISE ENCYCLOPEDIA OF SUPER-
SYMMETRY , Eds. S. Duplij, W.Siegel, J.Bagger, (Kluwer Acad. Publisher, Dordrecht Boston
London, 2003)
31

Curriculum Vitae Dmitri Maximovitch Guitman (Gitman)

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