Lorentz-violating effects in three-dimensional $QED$

TL;DR

This paper explores Lorentz-violating effects in a modified quantum electrodynamics model in 2+1 dimensions, analyzing its behavior at zero and finite temperature and its implications for higher-derivative terms and thermodynamics.

Contribution

It introduces a novel Lorentz-violating coupling in 2+1D QED and investigates its effects on the theory's structure and thermodynamical properties.

Findings

Spacetime dimensionality influences the radiative generation of higher-derivative terms.

The model exhibits unique features at finite temperature due to Lorentz violation.

Potential implications for nonminimal couplings in Lorentz-violating electrodynamics.

Abstract

Inspired in discussions presented lately regarding Lorentz-violating interaction terms in \cite{13,6}, we propose here a slightly different version for the coupling term. We will consider a modified quantum electrodynamics with violation of Lorentz symmetry defined in a $\left( 2+1\right) $-dimensional spacetime. We define the Lagrangian density with a Lorentz-violating interaction, where the the spacetime dimensionality is explicitly taken into account in its definition. The work encompasses an analysis of this model at both zero and finite-temperature, where very interesting features are known to occur due to the spacetime dimensionality. With that in mind we expect that the spacetime dimensionality may provide new insights about the radiative generation of higher-derivative terms into the action, implying in a new Lorentz-violating electrodynamics, as well the nonminimal coupling may provide interesting implications on the thermodynamical quantities.