Hierarchy of Dirac, Pauli and Klein-Gordon conserved operators in Taub-NUT background

TL;DR

This paper investigates the algebra of conserved observables for Dirac fermions in a Taub-NUT background, revealing connections between Dirac, Pauli, and Klein-Gordon operators to simplify analysis of their algebraic structures.

Contribution

It introduces a framework linking Dirac conserved operators with Pauli and Klein-Gordon operators in Taub-NUT space, enhancing understanding of their algebraic properties.

Findings

Conserved Dirac operators have physical parts related to Pauli operators.

Pauli operators are also conserved in Klein-Gordon theory.

Simplified methods for analyzing algebraic structures of conserved operators.

Abstract

The algebra of conserved observables of 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 Dirac conserved operators have physical parts associated with Pauli operators that are also conserved in the sense of the Klein-Gordon theory. In this way one gets simpler methods of analyzing the properties of the conserved Dirac operators and their main algebraic structures including the representations of dynamical algebras governing the Dirac quantum modes.