Induced Gauge Fields in the Path Integral

Abstract

The path integral on a homogeneous space $G/H$ is constructed, based on the guiding principle `first lift to $G$ and then project to $G/H$'. It is then shown that this principle admits inequivalent quantizations inducing a gauge field (the canonical connection) on the homogeneous space, and thereby reproduces the result obtained earlier by algebraic approaches.Comment: 12 pages, no figures, LaTe