The Dirac-Coulomb Problem for the $\kappa$-Poincare Quantum Group

TL;DR

This paper investigates the $ abla$-Poincare-Dirac equation in the context of the $ abla$-Dirac-Coulomb problem, showing first-order perturbations vanish and providing estimates for the quantum group parameter at second order.

Contribution

It introduces a gauged $ abla$-Poincare-Dirac equation for the $ abla$-Dirac-Coulomb problem and analyzes perturbations to understand quantum group effects.

Findings

First-order perturbation vanishes identically.

Second-order perturbation is singular but can be estimated with a cut-off.

Provides qualitative bounds on the quantum group parameter.

Abstract

The recently introduced $\kappa$-Poincare-Dirac equation is gauged to treat the $\kappa$-Dirac-Coulomb problem. For the resulting equation, we prove that the perturbation to first order in the quantum group parameter vanishes identically. The second order perturbation is singular, but assuming a heuristic cut-off allows a qualitative estimate of the quantum group parameter.