Exact Foldy-Wouthuysen transformation for a Dirac theory with the complete set ofCPT-Lorentz invariance violating terms

Abstract

The exact Foldy-Wouthuysen transformation is performed in order to study the Dirac field interacting with many possible external fields associated with $CPT$-Lorentz violation. We also derived the calculation of equations of motion as well as the generalized Lorentz force corrected by the mentioned external fields. The main point is the interaction between the Dirac particle and the terms that have the multiplication of the electromagnetic field and the terms that break $CPT$-Lorentz. Finally, with the transformed Hamiltonian we were able to write an expression for the bound state of the theory and analyze it in the atomic experiments context. This result is an analytical expression that gives the possibility of the weakness of $CPT$-Lorentz terms to be compensated by the presence of a strong magnetic field.