The time-dependent non-Abelian Aharonov-Bohm effect

TL;DR

This paper investigates the time-dependent non-Abelian Aharonov-Bohm effect, revealing a cancellation between electric and magnetic phase shifts in specific solutions, and suggesting this cancellation is a general feature of time-dependent gauge fields.

Contribution

It demonstrates the cancellation of phase shifts in time-dependent non-Abelian gauge fields using known solutions, extending understanding of the Aharonov-Bohm effect.

Findings

Cancellation between electric and magnetic phase shifts in non-Abelian fields.

Comparison of non-Abelian and Abelian time-dependent cancellations.

Postulation of a general cancellation mechanism in time-dependent gauge fields.

Abstract

In this article, we study the time-dependent Aharonov-Bohm effect for non-Abelian gauge fields. We use two well known time-dependent solutions to the Yang-Mills field equations to investigate the Aharonov-Bohm phase shift. For both of the solutions, we find a cancellation between the phase shift coming from the non-Abelian "magnetic" field and the phase shift coming from the non-Abelian "electric" field, which inevitably arises in time-dependent cases. We compare and contrast this cancellation for the time-dependent non-Abelian case to a similar cancellation which occurs in the time-dependent Abelian case. We postulate that this cancellation occurs generally in time-dependent situations for both Abelian and non-Abelian fields.