# Dimensional reduction of the electromagnetic sector of the nonminimal Standard-Model-Extension

## TL;DR

This paper develops a (1+2)-dimensional Lorentz-violating electrodynamics derived from the nonminimal SME in (1+3) dimensions, analyzing its properties, solutions, and potential applications in condensed matter physics.

## Contribution

It introduces a novel dimensional reduction of the nonminimal SME electromagnetic sector and explores its fundamental properties and solutions.

## Key findings

- Derived field equations and Green's functions for the reduced model
- Computed modified dispersion relations at leading order
- Removed unphysical gauge degrees of freedom

## Abstract

In the current paper, we construct a Lorentz-violating electrodynamics in (1+2) spacetime dimensions from the electromagnetic sector of the nonminimal Standard-Model Extension (SME) in (1+3) dimensions. Subsequently, we study some of the basic properties of this framework. We obtain the field equations, the Green's functions, and the perturbative Feynman rules. Furthermore, the modified dispersion relations are computed at leading order in Lorentz violation. We then remove the unphysical degrees of freedom from the electromagnetic Green's function that are present due to gauge invariance. The resulting object is used to construct the general solutions of the uncoupled field equations with external inhomogeneities present. This modified planar electrodynamics may be valuable to describe electromagnetic phenomena in two-dimensional condensed-matter systems. Furthermore, it supports a better understanding of the electromagnetic sector of the nonminimal SME.