Path Integrals on Riemannian Manifolds with Symmetry and Stratified Gauge Structure
| dc.creator | Tanimura, Shogo | |
| dc.date | 2001-10-02 | |
| dc.date.accessioned | 2026-07-07T04:12:27Z | |
| dc.date.available | 2026-07-07T04:12:27Z | |
| dc.description | 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. | |
| dc.description | 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 | |
| dc.identifier | https://arxiv.org/abs/hep-th/0110015 | |
| dc.identifier | http://arxiv.org/abs/hep-th/0110015 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/50908 | |
| dc.subject | High Energy Physics - Theory | |
| dc.subject | Mathematical Physics | |
| dc.subject | Differential Geometry | |
| dc.title | Path Integrals on Riemannian Manifolds with Symmetry and Stratified Gauge Structure | |
| dc.type | text |