Modified Dirac equation with Lorentz invariance violation and its solutions for particles in an external magnetic field

TL;DR

This paper introduces a modified Dirac equation incorporating Lorentz invariance violation, derives solutions for particles in magnetic fields, and estimates effects on synchrotron radiation, advancing understanding of Lorentz-violating quantum theories.

Contribution

It formulates a second-order modified Dirac equation with Lorentz violation, provides exact solutions in magnetic fields, and introduces a projection matrix for spin states.

Findings

Derived the modified dispersion relation due to Lorentz violation

Obtained exact solutions for particles in magnetic fields

Estimated the impact on synchrotron radiation radius

Abstract

The second-order modified Dirac equation leading to the modified dispersion relation due to the Lorentz invariance violation corrections is suggested. The equation is formulated in the 16-component first- order form. I have obtained the projection matrix extracting solutions of the equation with definite spin projections which can be considered as the density matrix for pure spin states. Exact solutions of the equation are found for particles in the external constant and uniform magnetic field. The synchrotron radiation radius within the novel modified Dirac equation is estimated.