Dirac equation, hydrogen atom spectrum and the Lamb shift in dynamical noncommutative spaces

TL;DR

This paper derives the hydrogen atom's relativistic Hamiltonian in dynamical noncommutative spaces, calculates energy shifts and the Lamb shift, and establishes bounds on the noncommutative parameter based on measurement accuracy.

Contribution

It introduces a relativistic Hamiltonian in dynamical noncommutative spaces and analyzes its effects on hydrogen atom spectra, including the Lamb shift, revealing differences from non-dynamical models.

Findings

Energy shifts depend on the dynamical noncommutative parameter { au}

Upper bounds on { au} are obtained from measurement accuracy

Both [2P]_{1/2} and [2S]_{1/2} levels are affected by noncommutativity

Abstract

We derive the relativistic Hamiltonian of hydrogen atom in dynamical noncommutative spaces (DNCS or {\tau}-space). Using this Hamiltonian we calculate the energy shift of the ground state and as well the [2P]_(1/2), [2S]_(1/2) levels. In all cases the energy shift depend on the dynamical noncommutative parameter {\tau}. Using the accuracy of the energy measurement we obtain an upper bound for {\tau}. We also study the lamb shift in DNCS. Both the levels [2P]_(1/2) and [2S]_(1/2) receive corrections due to dynamical noncommutativity of space which is in contrast to the non-dynamical noncommutative spaces (NDNCS or {\theta}-space) in which the level [2S]_(1/2) receives no correction.