AB effect and Aharonov-Susskind charge non-superselection

TL;DR

This paper examines the Aharonov-Bohm effect for particles in superpositions of different charge states, challenging the traditional charge superselection rule by analyzing gauge invariance and phase measurement ambiguities.

Contribution

It clarifies the conditions under which the Aharonov-Susskind phase can be observed, disputing the charge superselection rule through phase calibration considerations.

Findings

The Aharonov-Susskind phase can be measured without violating gauge invariance.

Charge superselection rule is not absolute; relative phases are physically meaningful.

Phase measurements depend on loop geometry around the magnetic flux.

Abstract

We consider a particle in a coherent superposition of states with different electric charge moving in the vicinity of a magnetic flux. Formally, it should acquire a (gauge-dependent) AB relative phase between the charge states, even for an incomplete loop. If measureable, such a geometric, rather than topological, AB-phase would seem to break gauge invariance. Wick, Wightman and Wigner argued that since (global) charge-dependent phase transformations are physically unobservable, charge state superpositions are unphysical (`charge superselection rule'). This would resolve the apparent paradox in a trivial way. However, Aharonov and Susskind disputed this superselection rule: they distinguished between such global charge-dependent transformations, and transformations of the relative inter-charge phases of two particles, and showed that the latter \emph{could} in principle be observable! Finally, the paradox again disappears once we considers the `calibration' of the phase measured by the Aharonov-Susskind phase detectors, as well as the phase of the particle at its initial point. It turns out that such a detector can only distinguish between the relative phases of two paths if their (oriented) difference forms a loop around the flux.