On geometric interpretation of the Aharonov-Bohm effect

TL;DR

This paper offers a geometric perspective on the Aharonov-Bohm effect, emphasizing the significance of connections on fiber bundles over topological considerations, and shows that nontrivial holonomy can occur even with trivial bundles.

Contribution

It introduces a geometric interpretation of the Aharonov-Bohm effect focusing on connections and holonomy, highlighting geometric effects over topological ones.

Findings

Principal fiber bundle can be trivial with nontrivial connection

Holonomy group captures the effect's essence

Geometric effects are more crucial than topological ones in this context

Abstract

A geometric interpretation of the Aharonov--Bohm effect is given in terms of connections on principal fiber bundles. It is demonstrated that the principal fiber bundle can be trivial while the connection and its holonomy group are nontrivial. Therefore, the main role is played by geometric rather than topological effects.