# On a Gambini-Pullin-inspired Maxwell electrodynamics with Lorentz-violating dimension-$5$ operators

## TL;DR

This paper investigates a Lorentz-violating extension of Maxwell electrodynamics with dimension-5 operators, revealing modified dispersion relations, vacuum birefringence, and connections to loop quantum gravity, with explicit equations for different background vectors.

## Contribution

It introduces a new Lorentz-violating Maxwell theory with higher-derivative terms, analyzing its physical implications and linking it to loop quantum gravity for specific background vectors.

## Key findings

- Modified dispersion relations exhibit vacuum birefringence.
- Equations of motion reproduce Gambini-Pullin electrodynamics for time-like backgrounds.
- Extended Maxwell equations derived for space-like Lorentz-violating vectors.

## Abstract

We explore the properties of a new Maxwell electrodynamics coupled to a Lorentz-violating background through the presence of higher-derivative terms. Physical implications of this alternative effective theory modified by Lorentz-violating operators of mass dimension-$5$ are considered, such as modified dispersion relations which exhibit the vacuum birefringence phenomenon. Subsequently, we analyze the energy-momentum tensor in the case we reproduce the Gambini-Pullin electrodynamics. We explicitly show that for a background time-like four-vector, $n^{\mu}$, the equations of motion indeed reproduce those encountered by Gambini and Pullin in the framework of loop quantum gravity . Finally, extended expressions for Maxwell-type equations are written down in the case the external Lorentz-violating four-vector is space-like.