Very Special Relativity and Lorentz Violating Theories

TL;DR

This paper explores Very Special Relativity (VSR), a mild Lorentz symmetry violation, by formulating a spinning particle model, coupling it to electromagnetic fields, and analyzing its effects on spin precession and magnetic moments.

Contribution

It introduces a systematic formulation of VSR effects in spinning particles and examines their impact on electromagnetic interactions and spin precession.

Findings

VSR terms modify the spin precession equations.

The model predicts VSR contributions to magnetic moments.

VSR effects are incorporated into a spinning particle framework.

Abstract

Very special relativity (VSR) keeps the main features of special relativity but breaks rotational invariance. It can not be regarded as a fundamental symmetry of nature because many observed phenomena depend on the existence of Lorentz boosts. However, within the scope of Lorentz violating theories it can have a role since it is breaking Lorentz symmetry in a very mild way. In this context, when VSR terms are incorporated in a Lorentz invariant theory several possibilities are allowed. In order to generate such terms systematically we start with a formulation for a spinning particle in VSR. It is then coupled minimally to the electromagnetic field and a gyromagnetic factor is added to give rise to a magnetic moment. In order to analyze the effects of VSR in Thomas precession a spin vector is then proposed in terms of the spinning particle variables. It is then found the VSR contributions to the equation which determines the spin precession angular velocity.