# Asymptotic charges, large gauge transformations and inequivalence of different gauges in external current QED

## TL;DR

This paper shows that in external current QED, different gauge choices lead to inequivalent quantum theories due to superselection sectors characterized by asymptotic electromagnetic flux, with large gauge transformations linked to the Aharonov-Bohm effect.

## Contribution

It demonstrates the non-unitary equivalence of different gauges in external current QED and relates large gauge transformations to physical flux and the Aharonov-Bohm effect.

## Key findings

- Different gauges correspond to inequivalent quantum theories.
- Spacelike asymptotic flux is a superselected quantity.
- Large gauge transformations are expressed via Wilson loops.

## Abstract

In this paper we consider external current QED in the Coulomb gauge and in axial gauges for various spatial directions of the axis. For a non-zero electric charge of the current, we demonstrate that any two different gauges from this class correspond to quantum theories which are not unitarily equivalent. We show that the spacelike asymptotic flux of the electromagnetic field is the underlying superselected quantity. We also express the large gauge transformation linking two distinct axial gauges by the Wilson loop over a contour limited by the two axes. Thus the underlying physical mechanism appears to be related to the Aharonov-Bohm effect.