Relativistic scalar Aharonov–Bohm scattering

Abstract

We discuss the scattering of relativistic spin zero particles by an infinitely long and arbitrarily thin solenoid. The exact solution of the first-quantized problem can be obtained as a mimic of the nonrelativistic case, either in the original Aharonov–Bohm way or by using the Berry magnetization scheme. The perturbative treatment is developed in the Feshbach–Villars two-component formalism for the Klein–Gordon equation and it is shown that it also requires renormalization as in the Schr¨odinger counterpart. The results are compared with those of the field theoretical approach, which corresponds to the two-body sector of the scalar Chern–Simons theory.