Path Integrals on Riemannian Manifolds with Symmetry and Stratified Gauge Structure
Abstract
We study a quantum system in a Riemannian manifold M on which a Lie group G acts isometrically. The path integral on M is decomposed into a family of path integrals on a quotient space Q=M/G and the reduced path integrals are completely classified by irreducible unitary representations of G. It is not necessary to assume that the action of G on M is either free or transitive. Hence the quotient space M/G may have orbifold singularities. Stratification geometry, which is a generalization of the concept of principal fiber bundle, is necessarily introduced to describe the path integral on M/G. Using it we show that the reduced path integral is expressed as a product of three factors; the rotational energy amplitude, the vibrational energy amplitude, and the holonomy factor.
Keywords
Cite
@article{arxiv.hep-th/0110015,
title = {Path Integrals on Riemannian Manifolds with Symmetry and Stratified Gauge Structure},
author = {Shogo Tanimura},
journal= {arXiv preprint arXiv:hep-th/0110015},
year = {2007}
}
Comments
10 pages, no figures, LaTeX2e; Proceedings of The Third International Conference on Geometry, Integrability and Quantization, which was held in June 14--23, 2001 in Bulgaria