Path Integrals on Riemannian Manifolds with Symmetry and Stratified Gauge Structure

Shogo Tanimura

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arXiv · hep-th/0110015

Path Integrals on Riemannian Manifolds with Symmetry and Stratified Gauge Structure

Shogo Tanimura

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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.

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Shogo Tanimura. 2001-10-02. Path Integrals on Riemannian Manifolds with Symmetry and Stratified Gauge Structure. https://arxiv.org/abs/hep-th/0110015

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