Noncommutative fields in three dimensions and mass generation

TL;DR

This paper explores how noncommutative field methods in three-dimensional gauge theories can generate or cancel the Chern-Simons term, revealing a duality between Maxwell and Maxwell-Chern-Simons theories.

Contribution

It demonstrates the generation and cancellation of the Chern-Simons term in three-dimensional gauge theories using noncommutative field techniques, showing a duality between different models.

Findings

Chern-Simons term generated in 3D electrodynamics via noncommutative fields

Chern-Simons term canceled in Maxwell-Chern-Simons theory at specific noncommutativity

Interchange between Maxwell and Maxwell-Chern-Simons theories demonstrated

Abstract

We apply the noncommutative fields method for gauge theory in three dimensions where the Chern-Simons term is generated in the three-dimensional electrodynamics. Under the same procedure, the Chern-Simons term is shown to be cancelled in the Maxwell-Chern-Simons theory for the appropriate value of the noncommutativity parameter. Hence the mutual interchange between Maxwell-Chern-Simons theory and pure Maxwell theory turns out to be generated within this method.