Finsler-like structures from Lorentz-breaking classical particles

TL;DR

This paper develops a method to derive classical particle Lagrangians from quartic dispersion relations, revealing new Lorentz-violating models linked to Finsler-like geometries, enhancing understanding of Lorentz-breaking effects.

Contribution

It introduces a novel approach to obtain classical Lagrangians from quartic dispersion relations, connecting Lorentz violation with Finsler-like geometries in flat spacetime.

Findings

Derived new Lagrangians for Lorentz-violating particles.

Identified morphisms related to field redefinitions.

Explored parallels with Finsler geometries.

Abstract

A method is presented for deducing classical point-particle Lagrange functions corresponding to a class of quartic dispersion relations. Applying this to particles violating Lorentz symmetry in the minimal Standard-Model Extension leads to a variety of novel lagrangians in flat spacetime. Morphisms in these classical systems are studied that echo invariance under field redefinitions in the quantized theory. The Lagrange functions found offer new possibilities for understanding Lorentz-breaking effects by exploring parallels with Finsler-like geometries.