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

¹  Instituto de Física Gleb Wataghin, UNICAMP - PO Box 6165, 13083-970, Campinas, SP, Brasil
²  Centro de Matemática, Computação e Cognição, Universidade Federal do ABC - 09210-170, Santo André, SP, Brazil

Corresponding authors: alexeb@ifi.unicamp.br roldao.rocha@ufabc.edu.br roldao@ifi.unicamp.br

Received: 3 October 2007
Accepted: 15 December 2007

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 (≡ (1, 0, 0, 1)), 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.