Proceedings of the International Conference on Geometry, Integrability and Quantization

Path Integrals on Riemannian Manifolds with Symmetry and Stratified Gauge Structure

Shogo Tanimura

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 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.

Article information

Source
Proceedings of the Third International Conference on Geometry, Integrability and Quantization, Ivaïlo M. Mladenov and Gregory L. Naber, eds. (Sofia: Coral Press Scientific Publishing, 2002), 431-441

Dates
First available in Project Euclid: 12 June 2015

Permanent link to this document
https://projecteuclid.org/ euclid.pgiq/1434145487

Digital Object Identifier
doi:10.7546/giq-3-2002-431-441

Mathematical Reviews number (MathSciNet)
MR1884865

Zentralblatt MATH identifier
1090.58502

Citation

Tanimura, Shogo. Path Integrals on Riemannian Manifolds with Symmetry and Stratified Gauge Structure. Proceedings of the Third International Conference on Geometry, Integrability and Quantization, 431--441, Coral Press Scientific Publishing, Sofia, Bulgaria, 2002. doi:10.7546/giq-3-2002-431-441. https://projecteuclid.org/euclid.pgiq/1434145487


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