Alternative classical Lagrangians for the Standard-Model Extension

TL;DR

This paper develops new classical relativistic Lagrangians for point particles in the Standard-Model Extension, enabling better modeling of Lorentz violation effects, including massless limits relevant for photons and potential applications in gravitational fields.

Contribution

It introduces alternative Lagrangians with well-defined massless limits for the SME, expanding the theoretical tools for modeling Lorentz violation in classical particles.

Findings

Lagrangians have well-defined massless limits.

Applicable to photon propagation in Lorentz-violating backgrounds.

Connections to Finsler geometry are suggested.

Abstract

The current paper introduces classical, relativistic Lagrangians for point-particle analogs to the field theory description of the Standard-Model Extension (SME) for Lorentz violation. Lagrangians of a form alternative to those derived and studied in previous works are in the spotlight. Interestingly, they have well-defined massless limits, which makes them suitable for describing classical-particle analogs of photons subject to Lorentz violation. We first deal with different types of Dirac fermion coefficients, followed by various configurations of the SME photon sector. The Lagrangians are accompanied by constraints that we treat properly using the techniques due to Dirac. The results encountered may find application in photon propagation through gravitational fields in the presence of spacetime symmetry violation. Connections to Finsler geometry are likely to exist.