101 research outputs found
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
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