Influence of Lorentz- and CPT-violating terms on the Dirac equation

TL;DR

This paper investigates how Lorentz- and CPT-violating terms affect the Dirac equation, revealing their impact on particle spectra and potential experimental signatures, especially in hydrogen spectral lines.

Contribution

It explicitly derives solutions and dispersion relations for the Dirac equation with Lorentz- and CPT-violating terms, analyzing their physical implications on hydrogen spectra.

Findings

Vector coupling yields no spectral modification.

Axial vector coupling causes Zeeman-like spectral splitting.

External fields do not introduce additional spectral changes.

Abstract

The influence of Lorentz- and CPT-violating terms (in "vector" and "axial vector" couplings) on the Dirac equation is explicitly analyzed: plane wave solutions, dispersion relations and eigenenergies are explicitly obtained. The non-relativistic limit is worked out and the Lorentz-violating Hamiltonian identified in both cases, in full agreement with the results already established in the literature. Finally, the physical implications of this Hamiltonian on the spectrum of hydrogen are evaluated both in the absence and presence of a magnetic external field. It is observed that the fixed background, when considered in a vector coupling, yields no qualitative modification in the hydrogen spectrum, whereas it does provide an effective Zeeman-like splitting of the spectral lines whenever coupled in the axial vector form. It is also argued that the presence of an external fixed field does not imply new modifications on the spectrum.