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

摘要

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