Local description of the Aharonov-Bohm effect with a quantum electromagnetic field

Pablo L. Saldanha

Published 2019-10-23Version 1

In the Aharonov-Bohm effect, the interference pattern formed by charged particles that propagate in an interferometer where the two possible paths enclose an infinite solenoid depends on the magnetic flux in the solenoid even if the particles only propagate in regions where the electromagnetic fields are zero. The usual interpretations are based on a local interaction of the gauge-dependent potential vector with the particles or on a nonlocal influence of the solenoid on the particles behavior. But here we show how the Aharonov-Bohm effect can be described as the result of virtual photon exchanges between the charged particles and the solenoid, where the particles and the solenoid interact locally with the quantum electromagnetic field. On this way, one of the the principal features of the electromagnetic field concept, which is to avoid action at a distance, is sustained with the Aharonov-Bohm effect. We predict a local and gauge-independent Aharonov-Bohm phase generation for the particles propagation in each path of the interferometer and provide an experimental proposal that could test this prediction.