Lyman-Alpha Spectroscopy in Non-Commutative Space-Time

TL;DR

This paper investigates how non-commutative space-time affects hydrogen atom energy levels and Lyman-alpha radiation, providing bounds on non-commutativity parameters and exploring potential astrophysical implications.

Contribution

It introduces a method to calculate non-commutative corrections to atomic energy levels and applies these to astrophysical phenomena, linking quantum geometry to cosmology.

Findings

Bounds on non-commutativity parameters from hydrogen spectral data

Predicted modifications to Lyman-alpha radiation due to non-commutativity

Potential influence of non-commutative geometry on cosmological observations

Abstract

Recently, there has been a certain amount of activity around the theme of cosmological and astrophysical applications of noncommutative geometry models of particle physics. We study space-time non-commutativity applied to the hydrogen atom and the corrections induced to transitions frequencies. By writing the Dirac equation for noncommutative Coulomb potential, we compute noncommutative corrections of the energy levels using perturbation methods and by comparing to the Lamb shift accuracy we get a bound on the parameter of non-commutativity. We use this bound to study the effects on the Lyman-{\alpha} ray and by induction look the possible influence of non-commutativity on some astrophysical and cosmological phenomena.