# Modified Maxwell equations from CPT-even Lorentz violation with Minimum Length

## TL;DR

This paper derives modified Maxwell equations incorporating CPT-even Lorentz violation and a minimum length scale, analyzing their effects in vacuum and media, and exploring implications for refractive index behavior.

## Contribution

It introduces a novel set of Maxwell equations modified by both Lorentz violation and minimum length, highlighting their combined impact on electromagnetic phenomena.

## Key findings

- Minimum length does not alter vacuum electromagnetic wave properties.
- In media, minimum length significantly modifies Maxwell equations.
- Refractive index depends on Lorentz violation and non-commutative parameters.

## Abstract

Here we discuss the presence of CPT-even Lorentz violation (LV) in the presence of a deformed Heisenberg algebra that leads to a minimum length (ML). We consider the case of a Maxwell lagrangian modified by the presence of a $K_{F}$ CPT-even LV theory and ML. We then derive a set of modified Maxwell equations in the cases of LV and ML and only ML. We verified that in the case of electromagnetic waves in the vacuum the presence of ML does not change the consequences of LV. On the other hand, in a material media ML changes the whole set of equations that can lead to important effects with respect to the usual equations. We also considered the more general case including LV and the modified equations in terms of matter fields. We then derived the refractive index as a function of the matter fields depending on LV and ML, and in particular we showed the behaviour of the refractive index with respect to the non-commutative parameter.