Dirac equation in very special relativity for hydrogen atom

TL;DR

This paper investigates how very special relativity (VSR) modifies the Dirac equation for a hydrogen atom, revealing non-local effects that lift energy degeneracies and setting bounds on VSR parameters.

Contribution

It derives a nonrelativistic Hamiltonian within VSR, showing novel non-local features and their impact on hydrogen atom energy levels.

Findings

VSR introduces non-local effects in the Dirac equation.

Energy level degeneracy in hydrogen is lifted by VSR corrections.

An upper bound on the VSR-parameter is established.

Abstract

In this work, we study the modified Dirac equation in the framework of very special relativity (VSR). The low-energy regime is accessed and the nonrelativistic Hamiltonian is obtained. It turns out that this Hamiltonian is similar to that achieved from the Standard Model Extension (SME) via coupling of the spinor field to a Lorentz-violating term, but new features arise inherited from the non-local character of the VSR. In addition, the implications of the VSR-modified Lorentz symmetry on the spectrum of a hydrogen atom are determined by calculating the first-order energy corrections in the context of standard quantum mechanics. Among the results, we highlight that the modified Hamiltonian provides non-vanishing corrections which lift the degeneracy of the energy levels and allow us to find an upper bound upon the VSR-parameter.