Relativistic scalar Aharonov-Bohm scattering

We discuss the scattering of relativistic spin zero particles by an infinit ely long and arbitrarily thin solenoid. The exact solution of the first-qua ntized problem can be obtained as a mimic of the nonrelativistic case, eith er in the original Aharonov-Bohm way or by using the Berry magnetization sc heme. The perturbative treatment is developed in the Feshbach-Villars two-c omponent formalism for the Klein-Gordon equation and it is shown that it al so requires renormalization as in the Schrodinger counterpart. The results are compared with those of the field theoretical approach, which correspond s to the two-body sector of the scalar Chern-Simons theory.