SO(4) symmetry in the relativistic hydrogen atom

TL;DR

This paper demonstrates that the relativistic hydrogen atom exhibits an SO(4) symmetry, which persists even with certain vector potentials, and discusses implications like the Lamb shift and symmetry breaking.

Contribution

It introduces a pseudo-spin vector operator to reveal SO(4) symmetry in the relativistic hydrogen atom, extending understanding of its symmetry properties.

Findings

SO(4) symmetry exists in the relativistic hydrogen atom

Symmetry persists with U(1) monopolar and nonabelian vector potentials

Lamb shift and symmetry breaking are analyzed

Abstract

We show that the relativistic hydrogen atom possesses an SO(4) symmetry by introducing a kind of pseudo-spin vector operator. The same SO(4) symmetry is still preserved in the relativistic quantum system in presence of an U(1) monopolar vector potential as well as a nonabelian vector potential. Lamb shift and SO(4) symmetry breaking are also discussed.