Lyman-Alpha Spectroscopy in Non-Commutative Space-Time

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.