Classical kinematics and Finsler structures for nonminimal Lorentz-violating fermions

TL;DR

This paper derives a classical Lagrangian for Lorentz-violating fermions based on the nonminimal SME, revealing two Finsler structures and enhancing understanding of classical descriptions in Lorentz-violating quantum theories.

Contribution

It introduces a classical Lagrangian for nonminimal SME fermions and identifies two novel Finsler structures associated with Lorentz violation.

Findings

One Finsler structure describes scaled Euclidean geometry.

The other Finsler structure is neither Riemannian nor Randers/Kropina.

Provides initial insights into classical Lagrangians in nonminimal SME fermion sector.

Abstract

In the current paper the Lagrangian of a classical, relativistic point particle is obtained whose conjugate momentum satisfies the dispersion relation of a quantum wave packet that is subject to Lorentz violation based on a particular coefficient of the nonminimal Standard-Model Extension (SME). The properties of this Lagrangian are analyzed and two corresponding Finsler structures are obtained. One structure describes a scaled Euclidean geometry, whereas the other is neither a Riemann nor a Randers or Kropina structure. The results of the article provide some initial understanding of classical Lagrangians of the nonminimal SME fermion sector.