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D. M. Gitman

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

At least 163 records · Page 9Linked to original sources
arXiv1998

Reparametrization Invariance as Gauge Symmetry

Reparametrization invariance being treated as a gauge symmetry shows some specific peculiarities. We study these peculiarities both from a general point of view and on concrete examples. We consider the canonical treatment of reparametrization invariant systems in which one fixes the gauge on the classical level by means of time-dependent gauge conditions. In such an approach one can interpret different gauges as different reference frames. We discuss the relations between different gauges and the problem of gauge invariance in this case. Finally, we establish a general structure of reparametrizations and its connection with the zero-Hamiltonian phenomenon.

hep-th↗
arXiv1998

Examples of D=11 S-supersymmetric actions for point-like dynamical systems

A non standard super extensions of the Poincare algebra (S-algebra [1,2]), which seems to be relevant for construction of various D=11 models, are studied. We present two examples of actions for point-like dynamical systems, which are invariant under off-shell closed realization of the S-algebra as well as under local fermionic $κ$-symmetry. On this ground, an explicit form of the S-algebra is advocated.

hep-th↗
arXiv1998

On zero modes of the eleven dimensional superstring

It is shown that recently pointed out by Berkovits on-shell degrees of freedom of the D=11 superstring do not make contributions into the quantum states spectrum of the theory. As a consequence, the spectrum coincides with that of the D=10 type IIA superstring.

hep-th↗
arXiv1997

Massless Wess-Zumino model as first quantized Siegel superparticle

It is shown that canonical quantization of the $4d$ Siegel superparticle yields massless Wess-Zumino model as an effective field theory. Quantum states of the superparticle are realized in terms of the real scalar superfields which prove to be decomposed into the sum of on-shell chiral and antichiral superfields.

hep-th↗
arXiv1997

Quantum scalar field in FRW Universe with constant electromagnetic background

We discuss massive scalar field with conformal coupling in Friedmann-Robertson-Walker (FRW) Universe of special type with constant electromagnetic field. Treating an external gravitational-electromagnetic background exactly, at first time the proper-time representations for out-in, in-in, and out-out scalar Green functions are explicitly constructed as proper-time integrals over the corresponding (complex) contours. The vacuum-to-vacuum transition amplitudes 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 investigated. The back reaction of the particles created to the electromagnetic field is estimated in different regimes. The connection between proper-time method and effective action is outlined. The effective action in scalar QED in weakly-curved FRW Universe (De Sitter space) with weak constant electromagnetic field is found as derivative expansion over curvature and electromagnetic field strength. Possible further applications of the results are briefly mentioned.

hep-th↗
arXiv1996

The effective potential of gauged NJL model in magnetic field

The formalism, which permits to study the phase structure of gauged NJL-model for arbitrary external fields, is developed. The effective potential in the gauged NJL model in the weak magnetic field is found. It is shown that in fixed gauge coupling case the weak magnetic field doesn't influence chiral symmetry breaking condition. The analogy with the situation near black hole is briefly mentioned.

hep-th↗
arXiv1996

Path Integrals and Pseudoclassical Description for Spinning Particles in Arbitrary Dimensions

The propagator of a spinning particle in external Abelian field and in arbitrary dimensions is presented by means of a path integral. The problem has different 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 effective action in the path integral has a form of the standard (Berezin-Marinov) pseudoclassical action. In odd dimensions the solution is presented for the first time and, in particular, it turns out that the gauge invariant part of the effective action differs 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 this action, we show that the operator quantization leads to adequate minimal quantum theory of spinning particles in odd dimensions. In contrast with the models proposed formerly in this case the new one admits both the operator and the path integral quantization. Finally the consideration is generalized for the case of the particle with anomalous magnetic moment.

hep-th↗
arXiv1996

Spin Factor in Path Integral Representation for Dirac Propagator in External Fields

We study the spin factor problem both in $3+1$ and $2+1$ dimensions which are essentially different 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 field. 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. {\bf B318} (1993) 122) which themselves need some additional justification. 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 configurations of external fields. Namely, in constant uniform electromagnetic field and in its combination with a plane wave field.

hep-th↗
arXiv1996

Chiral symmetry breaking in d=3 NJL model in external gravitational and magnetic fields

The phase structure of $d=3$ Nambu-Jona-Lasinio model in curved spacetime with magnetic field is investigated in the leading order of the $1/N$-expansion and in linear curvature approximation (an external magnetic field is treated exactly). The possibility of the chiral symmetry breaking under the combined action of the external gravitational and magnetic fields is shown explicitly. At some circumstances the chiral symmetry may be restored due to the compensation of the magnetic field by the gravitational field.

hep-th↗
arXiv1996

Proper time and path integral representations for the commutation function

On the example of the quantized spinor field, interacting with arbitrary external electromagnetic field, the commutation function is studied. It is shown that a proper time representation is available in any dimensions. Using it, all the light cone singularities of the function are found explicitly, generalizing the Fock formula in four dimensions, and a path integral representation is constructed.

hep-th↗
arXiv1996

Vacuum instability in external fields

We study particles creation in arbitrary space-time dimensions by external electric fields, in particular, by fields, which are acting for a finite time. The time and dimensional analysis of the vacuum instability is presented. It is shown that the distributions of particles created by quasiconstant electric fields can be written in a form which has a thermal character and seems to be universal. Its application, for example, to the particles creation in external constant gravitational field reproduces the Hawking temperature exactly.

hep-th↗
arXiv1996

Pseudoclassical description of the massive Dirac particles in odd dimensions

A pseudoclassical model is proposed to describe massive Dirac (spin one-half) particles in arbitrary odd dimensions. The quantization of the model reproduces the minimal quantum theory of spinning particles in such dimensions. A dimensional duality between the model proposed and the pseudoclassical description of Weyl particles in even dimensions is discussed.

hep-th↗
arXiv1996

Pseudoclassical description of higher spins in $2+1$ dimensions

Pseudoclassical supersymmetric model to describe massive particles with higher spins (integer and half-integer) in $2+1$ dimensions is proposed. The quantization of the model leads to the minimal (with only one polarization state) quantum theory. In particular, the Bargmann-Wigner type equations for higher spins arise in course of the canonical quantization. The cases of spin one-half and one are considered in detail. Here one gets Dirac particles and Chern-Simons particles respectively. A relation with the field theory is discussed. On the basis of the model proposed, and using dimensional reduction considerations, a model to describe Weyl particles with higher spins in $3+1$ dimensions is constructed.

hep-th↗
arXiv1995

Pseudoclassical model for Weyl particle in 10 dimensions

A pseudoclassical model to describe Weyl particle in 10 dimensions is proposed. In course of quantization both the massless Dirac equation and the Weyl condition are reproduced automatically. The construction can be relevant to Ramond-Neveu-Schwarz strings where the Weyl reduction in the Ramond sector has to be made by hand.

hep-th↗
arXiv1994

New Pseudoclassical model for Weyl particles

A new pseudoclassical model to describe Weyl particles is proposed. Different ways of its quantization are presented. They all lead to the theory of Weyl particle; namely, the massless Dirac equation and the Weyl condition are reproduced. In contrast with models discussed previously, this one admits both the Dirac quantization and quasicanonical quantization, with the fixation of almost all gauge freedom on the classical level.

hep-th↗
arXiv1994

Quantization of pseudoclassical model of spin one relativistic particle

A consistent procedure of canonical quantization of pseudoclassical model for spin one relativistic particle is considered. Two approaches to treat the quantization for the massless case are discussed, the limit of the massive case and independent quantization of a modified action. Quantum mechanics constructed for the massive case proves to be equivalent to the Proca theory and for massless case to the Maxwell theory. Results obtained are compared with ones for the case of spinning (spin one half) particle.

hep-th↗