Two-particle system in Coulomb potential for twist-deformed space-time

TL;DR

This paper investigates a two-particle Coulomb system in a twist-deformed space-time, deriving the Hamiltonian, and finds that noncommutativity effects on the ground state energy of Helium only appear at second order.

Contribution

It introduces a Hamiltonian formulation for a two-particle Coulomb system in twist-deformed space-time and analyzes the order of noncommutativity effects on energy corrections.

Findings

First-order corrections to Helium ground energy are zero.

Nontrivial effects of space-time noncommutativity appear at second order.

Hamiltonian expressed in commutative variables for analysis.

Abstract

In this article, we define two-particle system in Coulomb potential for twist-deformed space-time with spatial directions commuting to time-dependent function $f_{\kappa_a}({t})$. Particularly, we provide the proper Hamiltonian function and further, we rewrite it in terms of commutative variables. Besides, we demonstrate, that for small values of deformation parameters, the obtained in the perturbation framework, first-ordered corrections for ground Helium energy are equal to zero. In such a way we show, that nontrivial impact of space-time noncommutativity appears only at the second order of the quantum-mechanical correction expansion.