# Lorentz Violation and Riemann-Finsler Geometry

## TL;DR

This paper explores how Lorentz symmetry violations affect particle motion and geometric structures, deriving a class of Finsler spaces to model these effects in a charge-conserving scalar field theory.

## Contribution

It introduces a framework connecting Lorentz violation with Riemann-Finsler geometry, expanding the geometric understanding of Lorentz-violating theories.

## Key findings

- Derived a large class of Finsler spaces from Lorentz violation effects
- Analyzed properties of these Finsler spaces
- Linked Lorentz violation to modifications in particle dispersion relations

## Abstract

The general charge-conserving effective scalar field theory incorporating violations of Lorentz symmetry is presented. The dispersion relation is used to infer the effects of spin-independent Lorentz violation on point-particle motion. A large class of associated Finsler spaces is derived, and the properties of these spaces is explored.