Topological effects, dipole moments, and the dual current in 2+1 dimensions

We study the Aharonov-Casher effect and its electromagnetic-dual effect, introduced by He, McKellar, and Wilkens, 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 topological effects follow immediately. The restriction to 2+1 dimensions, with this interpretation, provides a unified way of treating these topological effects for an arbitrary spin, and a general proof for this case is provided. Perhaps more interestingly the treatment shows that a spin-0 particle can show these effects, although it has no magnetic or electric dipole moment in the usual sense.