Equivalence between Aharonov-Bohm and Aharonov-Casher effects, and motive forces

Abstract

Based on a gauge-theoretic approach, an equivalence between the Aharonov-Bohm effect of a solenoid and the Aharonov-Casher effect of a charged rod is explicitly demonstrated. It is shown that a time-dependent Aharonov-Casher phase can induce a motive force via the SU(2${)}_{\mathrm{spin}}$ gauge field. The intrinsic non-Abelian nature of the SU(2${)}_{\mathrm{spin}}$ gauge field predicts the non-Abelian Faraday law, subject to further experimental verification.