Does Dirac equation for a generalized Coulomb-like potential in D+1 dimensional flat spacetime admit any solution for $D\geq 4$?

TL;DR

This paper investigates the solutions of the Dirac equation for a generalized Coulomb potential in higher-dimensional spacetime and concludes that no physical solutions exist for dimensions four and above.

Contribution

It provides a numerical analysis of the radial Dirac equation in arbitrary dimensions and demonstrates the non-existence of physical solutions for D ≥ 4.

Findings

No physical solutions for D ≥ 4

Numerical solutions obtained for D < 4

Generalized Coulomb potential analyzed in higher dimensions

Abstract

The relativistic hydrogen atom in an Euclidean space-time of arbitrary number of space dimensions ($D$) plus one time dimension is revisited. In particular, numerical solutions of the radial Dirac equation for a generalized Coulombian potential proportional to $1/r^{(D-2)}$ are investigated. It is argued that one could not find any physical solution for $D\geq 4$.