Induced Gauge Fields in the Path Integral

TL;DR

This paper develops a path integral formulation on homogeneous spaces, demonstrating how different quantizations induce gauge fields and reproduce known algebraic results, thus linking geometric and algebraic quantization methods.

Contribution

It introduces a path integral approach that naturally induces gauge fields on homogeneous spaces, connecting geometric quantization with algebraic methods.

Findings

Path integral construction on $G/H$ space.

Induces gauge fields via inequivalent quantizations.

Reproduces algebraic quantization results.

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.