Relativistic Corrections to the Aharonov-Bohm Scattering
M. Gomes, J. M. C. Malbouisson, and A. J. da Silva
TL;DR
This paper investigates relativistic effects on Aharonov-Bohm scattering by expanding the two-body scattering amplitude in a quantum Chern-Simons scalar field theory, revealing that relativistic corrections modify the nonrelativistic scattering results.
Contribution
It provides the first detailed analysis of relativistic corrections to Aharonov-Bohm scattering within a Chern-Simons scalar field framework, extending previous nonrelativistic results.
Findings
Existence of a critical self-interaction parameter in the nonrelativistic limit.
Relativistic corrections modify the Aharonov-Bohm scattering amplitude.
Corrections are subdominant at leading order, appearing at relativistic order.
Abstract
We determine the |p|/m expansion of the two body scattering amplitude of the quantum theory of a Chern-Simons field minimally coupled to a scalar field with quartic self-interaction. It is shown that the existence of a critical value of the self-interaction parameter for which the 2-particle amplitude reduces to the Aharonov-Bohm one is restricted to the leading, nonrelativistic, order. The subdominant terms correspond to relativistic corrections to the Aharonov-Bohm scattering.
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