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

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.

10 pages

References in corpus (4)

• Signals for Lorentz Violation in Post-Newtonian Gravity
• Very Special Relativity
• Lorentz-violating dilatations in the momentum space and some extensions on non-linear actions of Lorentz algebra-preserving systems
• Dirac neutrino mass from the beta decay end-point modified by the dynamics of a Lorentz-violating equation of motion

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• Lorentz violating extension of the Standard Model and the Beta-decay end-point
• D-Oscillons in the Standard Model-Extension
• Spinor Fields, Singular Structures, Charge Conjugation, ELKO and Neutrino Masses
• Phenomenological Implications of Very Special Relativity
• k-deformed Poincare algebras and quantum Clifford-Hopf algebras
• The E(2) Particle
• Asymmetric particle-antiparticle Dirac equation: first quantization