Riemann-Finsler geometry and Lorentz-violating kinematics

TL;DR

This paper explores the connection between Lorentz-violating effective field theories and Riemann-Finsler geometry, presenting a new Finsler structure derived from a 1-form coefficient that complements the Randers structure.

Contribution

It introduces a novel Finsler structure constructed from a 1-form coefficient within the Standard-Model Extension, expanding the geometric understanding of Lorentz violation.

Findings

Identifies a new Finsler structure complementary to Randers geometry.

Links Lorentz violation in effective field theories to specific Riemann-Finsler geometries.

Provides an explicit example within the Standard-Model Extension framework.

Abstract

Effective field theories with explicit Lorentz violation are intimately linked to Riemann-Finsler geometry. The quadratic single-fermion restriction of the Standard-Model Extension provides a rich source of pseudo-Riemann-Finsler spacetimes and Riemann-Finsler spaces. An example is presented that is constructed from a 1-form coefficient and has Finsler structure complementary to the Randers structure.