Induced commutative Chern-Simons term from noncommutativity in planar systems

TL;DR

This paper investigates the consistency of noncommutative field theories for charged particles in strong magnetic fields by deriving the induced Chern-Simons term and confirming its agreement with known results.

Contribution

It demonstrates that a noncommutative matter field coupled to a U(1) gauge field induces a Chern-Simons term consistent with commutative calculations, validating the noncommutative approach.

Findings

Induced Chern-Simons term matches previous commutative results

Noncommutative description is consistent for charged particles in magnetic fields

Seiberg-Witten transformation relates noncommutative and commutative gauge fields

Abstract

We test the consistency of the use of a noncommutative theory description for charged particles in a strong magnetic field, by deriving the induced Chern-Simons (CS) term for an external Abelian gauge field in 2+1 dimensions. In this description, the system is modeled by a noncommutative matter field coupled to a U(1) noncommutative gauge field, related to the original, commutative one, by a Seiberg-Witten transformation. We show that an Abelian CS term for the commutative gauge field is indeed induced, and moreover that it matches the result of previous commutative field theory calculations.