Classical Lagrangians and Finsler structures for the nonminimal fermion sector of the Standard-Model Extension

TL;DR

This paper derives classical Lagrangians for the nonminimal fermion sector of the SME using algebraic methods, reanalyzes Lorentz violation tests, and explores connections to Finsler geometry, resulting in new constraints on SME coefficients.

Contribution

It introduces a method to derive classical Lagrangians for nonminimal SME operators and links these to Finsler geometry, providing new bounds on Lorentz violation coefficients.

Findings

Derived classical Lagrangians for nonminimal SME operators.

Reanalyzed historical Lorentz violation tests with new constraints.

Established connections between SME Lagrangians and Finsler geometry.

Abstract

This article is devoted to finding classical point-particle equivalents for the fermion sector of the nonminimal Standard-Model Extension (SME). For a series of nonminimal operators, such Lagrangians are derived at first order in Lorentz violation using the algebraic concept of Gr\"obner bases. Subsequently, the Lagrangians serve as a basis for reanalyzing the results of certain kinematic tests of Special Relativity that were carried out in the last century. Thereby, a number of new constraints on coefficients of the nonminimal SME is obtained. In the last part of the paper we point out connections to Finsler geometry.