Classical Lagrangians for the nonminimal spin-nondegenerate Standard-Model Extension at higher orders in Lorentz violation

TL;DR

This paper derives classical Lagrangians for spin-nondegenerate operators in the Standard-Model Extension, revealing complex dependencies on Lorentz violation and advancing understanding of particle behavior in Lorentz-violating backgrounds.

Contribution

It provides new classical Lagrangians for higher-order Lorentz-violating operators, filling a key gap in the theoretical description of particle propagation.

Findings

Derived Lagrangians for operators $ ext{b}_ ext{mu}$ and $ ext{H}_ ext{mu nu}$

Found peculiar functional dependence on background fields due to spin effects

Enhances modeling of particles in Lorentz-violating curved spacetimes

Abstract

We present new results for classical-particle propagation subject to Lorentz violation. Our analysis is dedicated to spin-nondegenerate operators of arbitrary mass dimension provided by the fermion sector of the Standard-Model Extension. In particular, classical Lagrangians are obtained for the operators $\hat{b}_{\mu}$ and $\hat{H}_{\mu\nu}$ as perturbative expansions in Lorentz violation. The functional dependence of the higher-order contributions in the background fields is found to be quite peculiar, which is probably attributed to particle spin playing an essential role for these cases. This paper closes one of the last gaps in understanding classical-particle propagation in the presence of Lorentz violation. Lagrangians of the kind presented will turn out to be valuable for describing particle propagation in curved backgrounds with diffeomorphism invariance and/or local Lorentz symmetry explicitly violated.