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Sergei V. Shabanov

Publications and source records attributed to Sergei V. Shabanov.

33 records · Page 2Linked to original sources
arXiv1998

BRST Inner Product Spaces and the Gribov Obstruction

A global extension of the Batalin-Marnelius proposal for a BRST inner product to gauge theories with topologically nontrivial gauge orbits is discussed. It is shown that their (appropriately adapted) method is applicable to a large class of mechanical models with a semisimple gauge group in the adjoint and fundamental representation. This includes cases where the Faddeev-Popov method fails. Simple models are found also, however, which do not allow for a well-defined global extension of the Batalin-Marnelius inner product due to a Gribov obstruction. Reasons for the partial success and failure are worked out and possible ways to circumvent the problem are briefly discussed.

hep-th↗
arXiv1998

The Inverse Variational Problem for Autoparallels

We study the problem of the existence of a local quantum scalar field theory in a general affine metric space that in the semiclassical approximation would lead to the autoparallel motion of wave packets, thus providing a deviation of the spinless particle trajectory from the geodesics in the presence of torsion. The problem is shown to be equivalent to the inverse problem of the calculus of variations for the autoparallel motion with additional conditions that the action (if it exists) has to be invariant under time reparametrizations and general coordinate transformations, while depending analytically on the torsion tensor. The problem is proved to have no solution for a generic torsion in four-dimensional spacetime. A solution exists only if the contracted torsion tensor is a gradient of a scalar field. The corresponding field theory describes coupling of matter to the dilaton field.

gr-qc↗
arXiv1998

Path Integral Quantization and Riemannian-Symplectic Manifolds

We develop a mathematically well-defined path integral formalism for general symplectic manifolds. We argue that in order to make a path integral quantization covariant under general coordinate transformations on the phase space and involve a genuine functional measure that is both finite and countably additive, the phase space manifold should be equipped with a Riemannian structure (metric). A suitable method to calculate the metric is also proposed.

quant-ph↗
arXiv1998

An Introduction to Coordinate-free Quantization and its Application to Constrained Systems

Canonical quantization entails using Cartesian coordinates, and Cartesian coordinates exist only in flat spaces. This situation can either be questioned or accepted. In this paper we offer a brief and introductory overview of how a flat phase space metric can be incorporated into a covariant, coordinate-free quantization procedure involving a continuous-time (Wiener measure) regularization of traditional phase space path integrals. Additionally we show how such procedures can be extended to incorporate systems with constraints and illustrate that extension for special systems.

quant-ph↗
arXiv1998

Constrained Systems and Analytical Mechanics in Spases with Torsion

A system with anholonomic constraints where the trajectories of physical degrees of freedom are autoparallels on a manifold equipped with a general Cartan connection is discussed. A variational principle for the autoparallel trajectories is derived from the d'Alambert-Lagrange principle for anholonomic constrained systems. A geometrical (coordinate-independent) formulation of the variational principle is given. Its relation to Sedov's anholonomic variational principle for dissipative systems and to Poincaré's variational principle in anholonomic reference frames is established. A modification of Noether's theorem due to the torsion force is studied. A non-local action whose extrema contain the autoparallels is proposed. The action can be made local by adding auxiliary degrees of freedom coupled to the original variables in a special way.

math-ph↗
arXiv1997

Supersymmetry in Stochastic Processes with Higher-Order Time Derivatives

A supersymmetric path integral representation is developed for stochastic processes whose Langevin equation contains any number N of time derivatives, thus generalizing the Langevin equation with inertia studied by Kramers, where N=2. The supersymmetric action contains N fermion fields with first-order time derivatives whose path integral is evaluated for fermionless asymptotic states.

quant-ph↗
arXiv1997

Coordinate-Free Quantization of Second-Class Constraints

The conversion of second-class constraints into first-class constraints is used to extend the coordinate-free path integral quantization, achieved by a flat-space Brownian motion regularization of the coherent-state path integral measure, to systems with second-class constraints.

hep-th↗
arXiv1997

Proper Dirac Quantization of Free Particle on D-Dimensional Sphere

We show that an unambiguous and correct quantization of the second-class constrained system of a free particle on a sphere in $D$ dimensions is possible only by converting the constraints to abelian gauge constraints, which are of first class in Dirac's classification scheme. The energy spectrum is equal to that of a pure Laplace-Beltrami operator with no additional constant arising from the curvature of the sphere. A quantization of Dirac's modified Poisson brackets for second-class constraints is also possible and unique, but must be rejected since the resulting energy spectrum is physically incorrect.

quant-ph↗
arXiv1996

The Monopole Dominance in QCD

A projection (gauge) independent formulation of the monopole dominance, discovered in lattice QCD for the maximal abelian projection, is given. A new dynamical abelian projection of continuum QCD, which does not rely on any explicit gauge condition imposed on gauge fields, is proposed. Under the assumption that the results of numerical simulations holds in the continuum limit, the monopole dominance is proved for the dynamical abelian projection. The latter enables us to develop an effective scalar field theory for dominant (monopole) configurations of gauge fields. The approach is manifestly gauge and Lorentz invariant.

hep-th↗
arXiv1996

Dynamical Abelian Projection of Gluodynamics

Assuming the monopole dominance, that has been proved in the lattice gluodynamics, to hold in the continuum limit, we develop an effective scalar field theory for QCD at large distances to describe confinement. The approach is based on a gauge (or projection) independent formulation of the monopole dominance and manifestly Lorentz invariant.

hep-th↗
arXiv1996

Abelian projection and studies of gauge-variant quantities in lattice QCD without gauge fixing

We suggest a new (dynamical) Abelian projection of the lattice QCD. It contains no gauge condition imposed on gauge fields so that Gribov copying is avoided. Configurations of gauge fields that turn into monopoles in the Abelian projection can be classified in a gauge invariant way. In the continuum limit, the theory respects the Lorentz invariance. A similar dynamical reduction of the gauge symmetry is proposed for studies of gauge-variant correlators (like a gluon propagator) in lattice QCD. Though the procedure is harder for numerical simulations, it is free of gauge fixing artifacts, like the Gribov horizon and copies.

hep-lat↗
arXiv1996

Supersymmetric quantization of gauge theories

We develop a new operator quantization scheme for gauge theories in which the dynamics of the ghost sector is described by an N=2 supersymmetry. In this scheme no gauge condition is imposed on the gauge fields. The corresponding path integral is explicitly Lorentz invariant and, in contrast to the BRST-BFV path integral in the Lorentz gauge, it is free of the Gribov ambiguity, i.e., it is also valid in the non-perturbative domain. The formalism can therefore be used to study the non-perturbative properties of gauge theories in the infra-red region (gluon confinement).

hep-th↗
arXiv1996

Coordinate-free quantization of first-class constrained systems

The coordinate-free formulation of canonical quantization, achieved by a flat-space Brownian motion regularization of phase-space path integrals, is extended to a special class of closed first-class constrained systems that is broad enough to include Yang-Mills type theories with an arbitrary compact gauge group. Central to this extension are the use of coherent state path integrals and of Lagrange multiplier integrations that engender projection operators onto the subspace of gauge invariant states.

hep-th↗