SPIN DEPENDENCE OF THE AHARONOV—BOHM EFFECT

Abstract

The problem of the proper inclusion of spin in Aharonov—Bohm scattering is considered. It is proposed that this should be accomplished by imposing the requirement that all singularities arising from the presence of spin in the associated wave equations be interpreted as limits of physically realizable flux distributions. This leads to results which confirm the usual cross section in the spinless case but imply nontrivial modifications for the scattering of a polarized spin one-half beam. By applying the technique to a calculation of the virial coefficient for a collection of flux carrying spin one-half particles, some severe obstacles to conventional views of the flux as a parameter which interpolates between bosonic and fermionic statistics are shown to occur. Although similar results for the scattering of arbitrary spin particles obtain in the Galilean limit, it is found that when spin one is considered in the context of a relativistic wave equation the singularity structure is too pathological to yield a consistent interpretation. The exact equivalence of the spin one-half Aharonov-Bohm effect to the Aharonov-Casher effect is also demonstrated and corresponding results for polarized beams are presented. Finally, it is shown that the Aharonov-Bohm effect for arbitrary spin in the Galilean limit is the exact solution in the two-particle sector of a Galilean covariant field theory.