Aharonov-Bohm Effect on Noncommutative Plane: A Coherent State Approach

TL;DR

This paper investigates the Aharonov-Bohm effect on a noncommutative plane using coherent states, revealing ultraviolet finiteness in scattering amplitudes and the need for self-interaction to recover the commutative limit.

Contribution

It introduces a coherent state approach to analyze the Aharonov-Bohm effect in noncommutative field theory, highlighting ultraviolet finiteness and the importance of self-interaction.

Findings

Scattering amplitude is ultraviolet finite in the noncommutative case.

Logarithmic singularities appear as the noncommutative parameter approaches zero.

Self-interaction is necessary for a smooth transition to the commutative limit.

Abstract

We apply the coherent state approach to study Aharonov-Bohm effect in the field theory context. We verify that, contrarily to the commutative result, the scattering amplitude is ultraviolet finite. However, we have logarithmic singularities as the noncommutative parameter tends to zero. Thus, the inclusion of a quartic self-interaction for the scalar field is necessary to obtain a smooth commutative limit.