English

AB effect and Aharonov-Susskind charge non-superselection

Quantum Physics 2015-05-18 v1

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.

Keywords

Cite

@article{arxiv.1003.1044,
  title  = {AB effect and Aharonov-Susskind charge non-superselection},
  author = {Noam Erez},
  journal= {arXiv preprint arXiv:1003.1044},
  year   = {2015}
}
R2 v1 2026-06-21T14:53:49.053Z