On the geometrical representation of the path integral reduction Jacobian: The case of dependent coordinates in the description of the reduced motion

The geometrical representation of the path integral reduction Jacobian obtained in the problem of the path integral quantization of a scalar particle motion on a smooth compact Riemannian manifold with the given free isometric action of the compact semisimple Lie group has been found for the case when the local reduced motion is described by means of dependent coordinates. The result is based on the scalar curvature formula for the original manifold which is viewed as a total space of the principal fibre bundle.Comment: 17 page

Vanishing Viscosity Method and Diffusion Processes

We construct diffusion processes associated with nonlinear parabolic equations and study their behavior as the viscosity (diffusion) coefficients go to zero. It allows to construct regularizations for solutions to hyperbolic equations and systems and study their vnishing viscosity limits

An approximation method for Navier-Stokes equations based on probabilistic approach

A new layer method solving the space-periodic problem for the Navier-Stokes equations is constructed by using probabilistic representations of their solutions. The method exploits the ideas of weak sense numerical integration of stochastic differential equations. Despite its probabilistic nature this method is nevertheless deterministic. A convergence theorem is proved

QED Revisited: Proving Equivalence Between Path Integral and Stochastic Quantization

We perform the stochastic quantization of scalar QED based on a generalization of the stochastic gauge fixing scheme and its geometric interpretation. It is shown that the stochastic quantization scheme exactly agrees with the usual path integral formulation.Comment: 11 page

On geometrical representation of the Jacobian in a path integral reduction problem

The geometrical representation of the Jacobian in the path integral reduction problem which describes a motion of the scalar particle on a smooth compact Riemannian manifold with the given free isometric action of the compact semisimple Lie group is obtained. By using the formula for the scalar curvature of the manifold with the Kaluza--Klein metric, we present the Jacobian as difference of the scalar curvature of the total space of the principal fibre bundle and the terms that are the scalar curvature of the orbit space, the scalar curvature of the orbit, the second fundamental form of the orbit and the square of the principle fibre bundle curvature.Comment: 8 page

Quantizing Yang-Mills Theory: From Parisi-Wu Stochastic Quantization to a Global Path Integral

Based on a generalization of the stochastic quantization scheme we recently proposed a generalized, globally defined Faddeev-Popov path integral density for the quantization of Yang-Mills theory. In this talk first our approach on the whole space of gauge potentials is shortly reviewed; in the following we discuss the corresponding global path integral on the gauge orbit space relating it to the original Parisi-Wu stochastic quantization scheme.Comment: 4 pages, Latex, uses espcrc2.sty; talk by Helmuth Huffel at the Third Meeting on Constrained Dynamics and Quantum Gravity, Villasimius, Sardinia, Italy, Sept. 13-17, 199