On the degeneracy of the energy levels of Schroedinger and Klein-Gordon equations on Riemannian coverings

TL;DR

This paper investigates how the degeneracy of energy levels in Schroedinger and Klein-Gordon equations varies on Riemannian coverings, influenced by parameters like cosmic strings, revealing lower degeneracy at non-integer values.

Contribution

It analyzes the impact of Riemannian coverings and the covering parameter on energy level degeneracy in quantum equations in curved space-times.

Findings

Degeneracy depends on the covering parameter k.

Lower degeneracy occurs at non-integer k values.

Superintegrability explains degeneracy patterns.

Abstract

We study the degeneracy of the energy levels of the Schroedinger equation with Kepler-Coulomb potential and of the Klein-Gordon equation on Riemannian coverings of the Euclidean space and of the Schwarzschild space-time respectively. Degeneracy of energy levels is a consequence of the superintegrability of the system. We see how the degree of degeneracy changes depending on the covering parameter k, the parameter that in space-times can be related with a cosmic string, and show examples of lower degeneracy in correspondence of non integer values of k.