New treatment of the noncommutative Dirac equation with a Coulomb potential

TL;DR

This paper derives a noncommutative Dirac equation with Coulomb potential using Seiberg-Witten maps, revealing modifications to energy levels and hyperfine structure, and providing a nonrelativistic hydrogen atom Hamiltonian.

Contribution

It introduces a novel approach to the noncommutative Dirac equation with Coulomb potential using modified Euler-Lagrange equations and Seiberg-Witten maps, highlighting new physical effects.

Findings

Noncommutativity modifies energy levels.

Hyperfine structure arises from noncommutative effects.

Nonrelativistic limit yields a generalized hydrogen atom Hamiltonian.

Abstract

Using the approach the modified Euler-Lagrange field equation together with the corresponding Seiberg-Witten maps of the dynamical fields, a noncommutative Dirac equation with a Coulomb potential is derived. We then find the noncommutative modification the energy levels and the possible new transitions. In the nonrelativistic limit a general form of the hamiltonian of the hydrogen atom is obtained, and we show that the noncommmutativity plays the role of spin and magnetic field which gives the hyper fine structure.