Classical kinematics for isotropic, minimal Lorentz-violating fermion operators

TL;DR

This paper develops a classical relativistic model for isotropic Lorentz-violating fermions, showing modified spin dynamics and trajectories, which facilitates studying such violations in curved spacetime.

Contribution

It introduces a classical Lagrangian framework for isotropic Lorentz-violating fermions, analyzing particle motion and spin evolution in external fields.

Findings

Particles follow scaled standard trajectories.

No spin precession occurs due to Lorentz violation.

Spin component transformation rates are modified.

Abstract

In this article the classical, relativistic Lagrangian based on the isotropic fermion sector of the Lorentz-violating (minimal) Standard-Model Extension is considered. The motion of the associated classical particle in an external electromagnetic field is studied and the evolution of its spin, which is introduced by hand, is investigated. It is shown that the particle travels along trajectories that are scaled versions of the standard ones. Furthermore there is no spin precession due to Lorentz violation, but the rate is modified at which the longitudinal and transverse spin components transform into each other. This demonstrates that it is practical to consider classical physics within such an isotropic Lorentz-violating framework and it opens the pathway to study a curved background in that context.