Transformation of the vector part of the 4-momentum in the Dirac equation and in Maxwell's equations in Majorana form for chiral media

Abstract

It is suggested to extend the results obtained for Maxwell's equations in Majorana form (spin-1 particles) for spin particles with a half-integer spin and a nonzero mass. It is shown that in an unbounded "chiral medium" (twisted media) the degeneration existing between particles of different helicities is removed. For ultrarelativistic particles, an analog to the inverse optical Magnus effect follows where the effect is determined by the chirality of the medium. From the inverse scattering problem for the transforms under consideration it follows that the amplitude of the wave function of a particle in a chiral medium can vary with time according to a linear law (for example, the process of neutrino (antineutrino) production or annihilation), and the parameters of the medium satisfy the evolution equation. © 2011 Springer Science+Business Media, Inc.