On the geometrical representation of the Jacobian in the path integral reduction problem
Copyright policy )On the geometrical representation of the Jacobian in the 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.
8 pages
- Institute for High Energy Physics Russian Federation
Diffusion processes and stochastic analysis on manifolds, 46T12; 65O30; 37J15; 53D20, Path integrals in quantum mechanics, Marsden-Weinstein reduction, 65O30, stochastic analysis, FOS: Physical sciences, Applications of stochastic analysis (to PDEs, etc.), 53D20, Mathematical Physics (math-ph), 46T12, Analysis on real and complex Lie groups, Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.), 37J15, path integral, Mathematical Physics
Diffusion processes and stochastic analysis on manifolds, 46T12; 65O30; 37J15; 53D20, Path integrals in quantum mechanics, Marsden-Weinstein reduction, 65O30, stochastic analysis, FOS: Physical sciences, Applications of stochastic analysis (to PDEs, etc.), 53D20, Mathematical Physics (math-ph), 46T12, Analysis on real and complex Lie groups, Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.), 37J15, path integral, Mathematical Physics
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