The Topological AC and HMW Effects, and the Dual Current in 2+1 Dimensions

Abstract

We study the Aharonov-Casher (AC) effect and the related He-McKellar-Wilkens (HMW) effect in 2+1 dimensions. In this restricted space these effects are the result of the interaction of the electromagnetic field tensor with the dual of a current. Transferring the dual operation from the current to the field tensor shows that this interaction may be reinterpreted as due to the interaction of an effective vector potential and a current, and the AC and HMW effects follow immediately. A general proof of this for particles with an arbitrary spin is provided. The restriction to 2+1 dimensions, with this interpretation, provides a unified way of treating the AC and HMW effects for an arbitrary spin. Perhaps more interestingly the treatment shows that a spin-0 particle can show AC and HMW effects, although it has no magnetic or electric dipole moment in the usual sense.