Obtaining the equation of motion for a fermionic particle in a generalized Lorentz-violating system frameworkA. E. Bernardini1 and R. da Rocha1, 2
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
received 3 October 2007; accepted in final form 15 December 2007; published February 2008
published online 28 January 2008
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)), n2 = 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.
03.30.+p - Special relativity.
11.30.Cp - Lorentz and Poincare invariance.
11.30.-j - Symmetry and conservation laws.
© EPLA 2008