A New Limit for the Non-Commutative Space-Time Parameter

TL;DR

This paper investigates the effects of space-time noncommutativity on the hydrogen atom, deriving bounds on the noncommutative parameter through theoretical analysis and comparison with experimental spectroscopy data.

Contribution

It introduces a novel approach to bound the noncommutative space-time parameter using hydrogen atom energy levels and phenomenological considerations.

Findings

Noncommutative effects mimic proton's extended charge distribution.

First-order effects are equivalent to an electron in a Coulomb and electric dipole field.

Second-order corrections to energy levels provide bounds consistent with experimental data.

Abstract

We study space-time noncommutativity applied to the hydrogen atom and the phenomenological aspects induced. We find that the noncommutative effects are similar to those obtained by considering the extended charged nature of the proton in the atom. To the first order in the noncommutative parameter, it is equivalent to an electron in the fields of a Coulomb potential and an electric dipole and this allows us to get a bound for the parameter. In a second step, we compute noncommutative corrections of the energy levels and find that they are at the second order in the parameter of noncommutativity. By comparing our results to those obtained from experimental spectroscopy, we get another limit for the parameter.