Berry Connections and Induced Gauge Fields in Quantum Mechanics on Sphere

TL;DR

This paper explores how Berry's connection manifests as a topological Chern-Simons term in the effective action of quantum mechanics on spheres, linking geometric phases to gauge fields.

Contribution

It demonstrates that Berry's connection appears as a Chern-Simons term in the effective action, connecting topological gauge fields with quantum mechanics on spheres.

Findings

Berry's connection acts as a topological term in the effective action.

The topological term is identified as a Chern-Simons term.

Gauge variables correspond to extra degrees of freedom in the enlarged space.

Abstract

Quantum mechanics on sphere $S^{n}$ is studied from the viewpoint that the Berry's connection has to appear as a topological term in the effective action. Furthermore we show that this term is the Chern-Simons term of gauge variables that correspond to the extra degrees of freedom of the enlarged space.