Higher derivative Chern-Simons extension in the noncommutative QED$_{3}$

TL;DR

This paper investigates the one-loop effective action in noncommutative QED3, revealing how higher-derivative corrections modify the NC Chern-Simons theory and analyzing their impact on gauge invariance and photon propagator poles.

Contribution

It introduces higher-derivative modifications to the noncommutative Chern-Simons action and examines their effects on gauge invariance and photon propagator corrections.

Findings

One-loop effective action yields NC Chern-Simons and Maxwell terms at large fermion mass.

Higher-derivative contributions to NC Chern-Simons are explicitly derived.

One-loop correction affects the pole of the photon propagator.

Abstract

The noncommutative (NC) massive quantum electrodynamics in $2+1$ dimensions is considered. We show explicitly that the one-loop effective action arising from the integrating out the fermionic fields leads to the ordinary NC Chern-Simons and NC Maxwell action at the long wavelength limit (large fermion mass). In the next to leading order, the higher-derivative contributions to NC Chern-Simons are obtained. Moreover, the gauge invariance of the outcome action is carefully discussed. We then consider the higher-derivative modification into the pure NC Chern-Simons Lagrangian density and evaluate the one-loop correction to the pole of the photon propagator.