Relativistic scalar Aharonov-Bohm scattering

TL;DR

This paper analyzes relativistic scalar particle scattering by an infinitely thin solenoid, providing exact solutions, perturbative approaches with renormalization, and comparisons with field theory, extending the nonrelativistic Aharonov-Bohm effect.

Contribution

It offers a comprehensive analysis of relativistic scalar Aharonov-Bohm scattering, including exact solutions, perturbative methods with renormalization, and comparison with field-theoretic models, which is novel in this context.

Findings

Exact solutions for relativistic scattering are obtained.

Perturbative treatment requires renormalization similar to nonrelativistic case.

Results align with scalar Chern-Simons field theory predictions.

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's 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 Schrodinger 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.