Obtaining the equation of motion for a fermionic particle in a generalized Lorentz-violating system framework

TL;DR

This paper derives the equation of motion for fermions in a Lorentz-violating framework, showing energy-dependent behavior that reduces to known equations and suggesting experimental tests for Lorentz violation effects.

Contribution

It introduces a generalized method for deriving fermionic equations of motion in Lorentz-violating systems, clarifying behavior at different energy scales and analyzing symmetry modifications.

Findings

At high energies, the equation reduces to a chiral lepton number conserving form.

At low energies, it simplifies to the standard Dirac equation.

Proposes feasible experiments to detect Lorentz-violating effects.

Abstract

Using a generalized procedure for obtaining the dispersion relation and the equation of motion for a propagating fermionic particle, we examine previous claims for a preferred axis at $n_{\mu}$($\equiv(1,0,0,1)$), $n^{2}=0$ embedded in the framework of very special relativity (VSR). We show that, in a relatively high energy scale, the corresponding equation of motion is reduced to a conserving lepton number chiral equation previously predicted in the literature. Otherwise, in a relatively low energy scale, the equation is reduced to the usual Dirac equation for a free propagating fermionic particle. It is accomplished by the suggestive analysis of some special cases where a nonlinear modification of the action of the Lorentz group is generated by the addition of a modified conformal transformation which, meanwhile, preserves the structure of the ordinary Lorentz algebra in a very peculiar way. Some feasible experiments, for which Lorentz violating effects here pointed out may be detectable, are suggested.