Noncommutative Field Theory: Nonrelativistic Fermionic Field Coupled to the Chern-Simons Field in 2+1 Dimensions

TL;DR

This paper investigates a noncommutative nonrelativistic fermionic field theory in 2+1 dimensions coupled with the Chern-Simons field, demonstrating divergence cancellations up to one loop due to noncommutative effects.

Contribution

It provides a perturbative analysis showing divergence cancellations in a noncommutative fermionic Chern-Simons theory, highlighting the role of the noncommutative Pauli term.

Findings

Ultraviolet divergences are canceled at one loop.

Infrared divergences are eliminated by the noncommutative Pauli term.

The model remains consistent at the quantum level up to one loop.

Abstract

We study a noncommutative nonrelativistic fermionic field theory in 2+1 dimensions coupled to the Chern-Simons field. We perform a perturbative analysis of model and show that up to one loop the ultraviolet divergences are canceled and the infrared divergences are eliminated by the noncommutative Pauli term.