Noncommutative of space-time and the relativistic Hydrogen atom

TL;DR

This paper investigates the effects of noncommutative space-time on the relativistic Hydrogen atom, deriving energy level corrections and establishing bounds on noncommutativity parameters through comparison with experimental transition data.

Contribution

It introduces a second-order correction analysis of the Klein-Gordon equation in noncommutative space-time applied to hydrogen, linking noncommutativity to observable spectral shifts.

Findings

Bound on noncommutativity parameter from spectral data

Noncommutativity as a source of Lamb shift corrections

Identification of spin effects due to noncommutativity

Abstract

We study the Klein-Gordon equation in a non-commutative space-time as applied to the Hydrogen atom to extract the energy levels, by considering the second-order corrections in the non-commutativity paramete and by comparing to the 2S - 1S transition accuracy we get a bound on the parameter of noncommutativity. Phenomenologically we show that non-commutativity is the source of lamb shift corrections and spin electron.