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D. M. Gitman

Publications and source records attributed to D. M. Gitman.

At least 145 records · Page 8Linked to original sources
arXiv2001

Constraint Reorganization Consistent with the Dirac Procedure

The way of finding all the constraints in the Hamiltonian formulation of singular (in particular, gauge) theories is called the Dirac procedure. The constraints are naturally classified according to the correspondig stages of this procedure. On the other hand, it is convenient to reorganize the constraints such that they are explicitly decomposed into the first-class and second-class constraints. We discuss the reorganization of the constraints into the first- and second-class constraints that is consistent with the Dirac procedure, i.e., that does not violate the decomposition of the constraints according to the stages of the Dirac procedure. The possibility of such a reorganization is important for the study of gauge symmetries in the Lagrangian and Hamiltonian formulations.

hep-th↗
arXiv2001

Aspects of Two-Level Systems under External Time Dependent Fields

The dynamics of two-level systems in time-dependent backgrounds is under consideration. We present some new exact solutions in special backgrounds decaying in time. On the other hand, following ideas of Feynman, Vernon and Hellwarth, we discuss in detail the possibility to reduce the quantum dynamics to a classical Hamiltonian system. This, in particular, opens the possibility to directly apply powerful methods of classical mechanics (e.g. KAM methods) to study the quantum system. Following such an approach, we draw conclusions of relevance for ``quantum chaos'' when the external background is periodic or quasi-periodic in time.

quant-ph↗
arXiv2001

New solutions of relativistic wave equations in magnetic fields and longitudinal fields

We demonstrate how one can describe explicitly the present arbitrariness in solutions of relativistic wave equations in external electromagnetic fields of special form. This arbitrariness is connected to the existence of a transformation, which reduces effectively the number of variables in the initial equations. Then we use the corresponding representations to construct new sets of exact solutions, which may have a physical interest. Namely, we present new sets of stationary and nonstationary solutions in magnetic field and in some superpositions of electric and magnetic fields.

hep-th↗
arXiv2001

Quantization of spinning particle in arbitrary background

The article is a natural continuation of the papers by Gavrilov and Gitman (Class.Quant.Grav. {\bf 17} (2000) L133; Int. J. Mod. Phys. A15 (2000) 4499) devoted to relativistic particle quantization. Here we generalize the problem, considering the quantization of a spinning particle in arbitrary gravitational background. The nontriviality of such a generalization is related to the neccessity of solving complicated ordering problems. Similar to the flat space-time case, we show in the course of the canonical quantization how a consistent relativistic quantum mechanics of spinning particle in gravitational and electromagnetic backgrounds can be constructed.

hep-th↗
arXiv2000

Aharonov-Bohm Effect in Cyclotron and Synchrotron Radiations

We study the impact of Aharonov-Bohm solenoid on the radiation of a charged particle moving in a constant uniform magnetic field. With this aim in view, exact solutions of Klein-Gordon and Dirac equations are found in the magnetic-solenoid field. 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 effect 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

hep-th↗
arXiv2000

Fields on the Poincare group: arbitrary spin description and relativistic wave equations

In this paper, starting from pure group-theoretical point of view, we develop a regular approach to describing particles with different spins in the framework of a theory of scalar fields on the Poincare group. Such fields can be considered as generating functions for conventional spin-tensor fields. The cases of 2, 3, and 4 dimensions are elaborated in detail. Discrete transformations $C,P,T$ are defined for the scalar fields as automorphisms of the Poincare group. Doing a classification of the scalar functions, we obtain relativistic wave equations for particles with definite spin and mass. There exist two different types of scalar functions (which describe the same mass and spin), one related to a finite-dimensional nonunitary representation and another one related to an infinite-dimensional unitary representation of the Lorentz subgroup. This allows us to derive both usual finite-component wave equations for spin-tensor fields and positive energy infinite-component wave equations.

hep-th↗
arXiv2000

Discrete symmetries as automorphisms of the proper Poincare group

We present the consistent approach to finding the discrete transformations in the representation spaces of the proper Poincaré group. To this end we use the possibility to establish a correspondence between involutory automorphisms of the proper Poincaré group and the discrete transformations. As a result, we derive rules of the discrete transformations for arbitrary spin-tensor fields without the use of relativistic wave equations. Besides, we construct explicitly fields carrying representations of the extended Poincaré group, which includes the discrete transformations as well.

hep-th↗
arXiv2000

Equations of Motion for Massive Spin 2 Field Coupled to Gravity

We investigate the problems of consistency and causality for the equations of motion describing massive spin two field in external gravitational and massless scalar dilaton fields in arbitrary spacetime dimension. From the field theoretical point of view we consider a general classical action with non-minimal couplings and find gravitational and dilaton background on which this action describes a theory consistent with the flat space limit. In the case of pure gravitational background all field components propagate causally. We show also that the massive spin two field can be consistently described in arbitrary background by means of the lagrangian representing an infinite series in the inverse mass. Within string theory we obtain equations of motion for the massive spin two field coupled to gravity from the requirement of quantum Weyl invariance of the corresponding two dimensional sigma-model. In the lowest order in $α'$ we demonstrate that these effective equations of motion coincide with consistent equations derived in field theory.

hep-th↗
arXiv2000

Causality of Massive Spin 2 Field in External Gravity

We investigate the structure of equations of motion and lagrangian constraints in a general theory of massive spin 2 field interacting with external gravity. We demonstrate how consistency with the flat limit can be achieved in a number of specific spacetimes. One such example is an arbitrary static spacetime though equations of motion in this case may lack causal properties. Another example is provided by external gravity fulfilling vacuum Einstein equations with arbitrary cosmological constant. In the latter case there exists one-parameter family of theories describing causal propagation of the correct number of degrees of freedom for the massive spin 2 field in arbitrary dimension. For a specific value of the parameter a gauge invariance with a vector parameter appears, this value is interpreted as massless limit of the theory. Another specific value of the parameter produces gauge invariance with a scalar parameter and this cannot be interpreted as a consistent massive or massless theory.

hep-th↗
arXiv2000

Quantization of the Relativistic Particle

We revise the problem of the quantization of relativistic particle, presenting a modified consistent canonical scheme, which 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 field. At the same time this construction presents a possible solution of the well-known old problem how to construct a consistent quantum mechanics on the base of a relativistic wave equation.

hep-th↗
arXiv2000

QED in external field with space-time uniform invariants. Exact solutions

We study exact solutions of Dirac and Klein-Gordon equations and Green functions in d-dimensional QED and in an external electromagnetic field with constant and homogeneous field invariants. The cases of even and odd dimensions are considered separately, they are essentially different. We direct attention to the asymmetry of the quasienergy spectrum, which appears in odd dimensions. The in and out classification of the exact solutions as well as the completeness and orthogonality relations is strictly proven. Different Green functions in the form of sums over the exact solutions are constructed. The Fock-Schwinger proper time integral representations of these Green functions are found. As physical applications we consider the calculations of different quantum effects related to the vacuum instability in the external field. For example, we present mean values of particles created from the vacuum, the probability of the vacuum remaining a vacuum, the effective action, and the expectation values of the current and energy-momentum tensor.

hep-th↗
arXiv2000

Quantization of Point-Like Particles and Consistent Relativistic Quantum Mechanics

We revise the problem of the quantization of relativistic particle models (spinless and spinning), presenting a modified consistent canonical scheme. One of the main point of the modification 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 field. 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.

hep-th↗
arXiv2000

Quantum spinor field in the FRW universe with a constant electromagnetic background

The article is a natural continuation of our paper {\em Quantum scalar field in FRW Universe with constant electromagnetic background}, Int. J. Mod. Phys. {\bf A12}, 4837 (1997). We generalize the latter consideration to the case of massive spinor field, which is placed in FRW Universe of special type with a constant electromagnetic field. To this end special sets of exact solutions of Dirac equation in the background under consideration are constructed and classified. Using these solutions representations for out-in, in-in, and out-out spinor Green functions are explicitly constructed as proper-time integrals over the corresponding contours in complex proper-time plane. The vacuum-to-vacuum transition amplitude and number of created particles are found and vacuum instability is discussed. The mean values of the current and energy-momentum tensor are evaluated, and different approximations for them are presented. The back reaction related to particle creation and to the polarization of the unstable vacuum is estimated in different regimes.

hep-th↗
arXiv1999

Covariant Quantization with Extended BRST Symmetry

A short rewiev of covariant quantization methods based on BRST-antiBRST symmetry is given. In particular problems of correct definition of Sp(2) symmetric quantization scheme known as triplectic quantization are considered.

hep-th↗
arXiv1999

Green-Schwarz type formulation of D=11 S - invariant superstring and superparticle actions

A manifestly Poincare invariant formulations for $SO(1,10)$ and SO(2,9) superstring actions are proposed. The actions are invariant under a local fermionic $κ$-symmetry as well as under a number of global symmetries, which turn out to be on-shell realization of the known ``new supersymmetry`` S-algebra. Canonical quantization of the theory is performed and relation of the quantum state spectrum with that of type IIA Green-Schwarz superstring is discussed. Besides, a mechanical model is constructed, which is a zero tension limit of the D=11 superstring and which incorporates all essential features of the latter. A corresponding action invariant under off-shell closed realization of the S-algebra is obtained.

hep-th↗
arXiv1998

Classical description of spinning degrees of freedom of relativistic particles by means of commuting spinors

We consider a possibility to describe spin one-half and higher spins of massive relativistic particles by means of commuting spinors. We present two classical gauge models with the variables $x^μ,ξ_α,χ_α$, where $ξ,χ$ are commuting Majorana spinors. In course of quantization both models reproduce Dirac equation. We analyze the possibility to introduce an interaction with an external electromagnetic background into the models and to generalize them to higher spin description. The first model admits a minimal interaction with the external electromagnetic field, but leads to reducible representations of the Poincare group being generalized for higher spins. The second model turns out to be appropriate for description of the massive higher spins. However, it seams to be difficult to introduce a minimal interaction with an external electromagnetic field into this model. We compare our approach with one, which uses Grassman variables, and establish a relation between them.

hep-th↗
arXiv1998

A Modified Scheme of Triplectic Quantization

A modified version of triplectic quantization, first introduce by Batalin and Martnelius, is proposed which makes use of two independent master equations, one for the action and one for the gauge functional such that the initial classical action also obeys that master equation.

hep-th↗