The canonical connection in quantum mechanics

TL;DR

This paper explores how gauge fields naturally emerge in quantum systems on coset spaces, linking G-invariance to induced gauge fields and extending to non-abelian Berry phases in systems with slow variables.

Contribution

It demonstrates the role of G-invariance in the emergence of induced gauge fields and connects this to non-abelian Berry phases in quantum systems with coset space variables.

Findings

G-invariance is key to the emergence of H-connection in quantum sectors

Induced gauge fields appear in quantum mechanics on coset spaces

Non-abelian Berry phases can be derived from these gauge structures

Abstract

In this paper we investigate the form of induced gauge fields that arises in two types of quantum systems. In the first we consider quantum mechanics on coset spaces G/H, and argue that G-invariance is central to the emergence of the H-connection as induced gauge fields in the different quantum sectors. We then demonstrate why the same connection, now giving rise to the non-abelian generalization of Berry's phase, can also be found in systems which have slow variables taking values in such a coset space.