Noncommutative Correction to the Aharonov-Bohm Scattering: a Field Theory Approach

TL;DR

This paper investigates how noncommutative geometry modifies the Aharonov-Bohm scattering in a 2+1 dimensional scalar-Chern-Simons field theory, showing that noncommutativity affects renormalizability and scattering corrections.

Contribution

It introduces a noncommutative field theory model for Aharonov-Bohm effect and analyzes one-loop corrections, highlighting differences from the commutative case and the necessity of specific self-interactions.

Findings

Noncommutative model remains finite at one-loop for small noncommutativity.

Quartic self-interaction is not needed for renormalizability in noncommutative case.

Corrections to Aharonov-Bohm scattering are explicitly calculated.

Abstract

We study a noncommutative nonrelativistic theory in 2+1 dimensions of a scalar field coupled to the Chern-Simons field. In the commutative situation this model has been used to simulate the Aharonov-Bohm effect in the field theory context. We verified that, contrarily to the commutative result, the inclusion of a quartic self-interaction of the scalar field is not necessary to secure the ultraviolet renormalizability of the model. However, to obtain a smooth commutative limit the presence of a quartic gauge invariant self-interaction is required. For small noncommutativity we fix the corrections to the Aharonov-Bohm scattering and prove that up to one-loop the model is free from dangerous infrared/ultraviolet divergences.