Dynamical algebra and Dirac quantum modes in Taub-NUT background

TL;DR

This paper explores the algebraic structure of Dirac fermions in a Taub-NUT background, revealing how their quantum modes are governed by a specific dynamical algebra, leading to unique discrete modes with no separated variables.

Contribution

It demonstrates that the discrete quantum modes in Taub-NUT space are described by reducible representations of the o(4) algebra, connecting algebraic structures with quantum solutions.

Findings

Discrete modes governed by o(4) algebra

Existence of central and axial discrete modes

Spinors with no separated variables

Abstract

The SO(4,1) gauge-invariant theory of the Dirac fermions in the external field of the Kaluza-Klein monopole is investigated. It is shown that the discrete quantum modes are governed by reducible representations of the o(4) dynamical algebra generated by the components of the angular momentum operator and those of the Runge-Lenz operator of the Dirac theory in Taub-NUT background. The consequence is that there exist central and axial discrete modes whose spinors have no separated variables.