The Exact Foldy-Wouthuysen Transformation for a Dirac Theory with the complete set of CPT-Lorentz violating terms

TL;DR

This paper performs an exact Foldy-Wouthuysen transformation on a Dirac theory with CPT-Lorentz violating terms, deriving equations of motion and analyzing atomic bound states to explore experimental implications.

Contribution

It provides an analytical transformation of the Dirac Hamiltonian including CPT-Lorentz violation, enabling detailed study of external field interactions and atomic bound states.

Findings

Derived the exact transformed Hamiltonian with CPT-Lorentz violation.

Formulated equations of motion and generalized Lorentz force.

Analyzed atomic bound states considering external fields and CPT-Lorentz 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 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.