Remarks on Finsler Geometry and Lorentz Violation

TL;DR

This paper explores the connection between Finsler geometry and Lorentz violation in spacetime physics, highlighting recent developments in calculable Finsler structures derived from Lorentz-violating Lagrange functions within the Standard-Model Extension framework.

Contribution

It provides a summary of recent results and introduces new calculable Finsler structures based on Lorentz-violation Lagrange functions.

Findings

Identification of Finsler structures in Lorentz-violating physics

Development of new calculable Finsler models

Insights into classical particle dynamics in Lorentz-violating spacetime

Abstract

The physics of classical particles in a Lorentz-breaking spacetime has numerous features resembling the properties of Finsler geometry. In particular, the Lagrange function plays a role similar to that of a Finsler structure function. A summary is presented of recent results, including new calculable Finsler structures based on Lagrange functions appearing in the Lorentz-violation framework known as the Standard-Model Extension.