Non-Abelian Aharonov-Bohm effect with the time-dependent gauge fields

TL;DR

This paper studies the non-Abelian Aharonov-Bohm effect with time-dependent gauge fields and finds that the phase shift vanishes at first order, implying flux quantization does not occur in such scenarios.

Contribution

It demonstrates that the non-Abelian AB phase shift vanishes at first order for time-dependent gauge fields, clarifying the behavior of flux quantization in dynamic contexts.

Findings

Non-Abelian AB phase shift vanishes at first order for time-dependent fields.

Flux quantization does not occur in time-dependent Abelian or non-Abelian AB effects.

Electric and magnetic fields in the adjoint representation do not produce a phase shift at first order.

Abstract

We investigate the non-Abelian Aharonov-Bohm (AB) effect for time-dependent gauge fields. We prove that the non-Abelian AB phase shift related to time-dependent gauge fields, in which the electric and magnetic fields are written in the adjoint representation of $SU(N)$ generators, vanishes up to the first order expansion of the phase factor. Therefore, the flux quantization in a superconductor ring does not appear in the time-dependent Abelian or non-Abelian AB effect.