Dynamical algebra and Dirac quantum modes in the Taub-NUT background

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.Pacs 04.62.+v

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

“…In this way we show that the results of Ref. 9 hold also in the case of continuous energy spectra, for so (3,1) or e(3) dynamical algebras. The conclusions and comments are presented in the last section and in a short Appendix some formulas involving an important Pauli operator studied in Refs.…”

“…We start in the second section with a brief review of some previous results [7][8][9] we need. In the next section we study the algebra of the conserved Dirac operators and introduce a new type of even operators which help us to define the projection operator that separates the physical parts.…”

Dirac-Type Operators on Curved Spaces and the Role of Killing-Yano Tensors

“…In the case of the Dirac equation, the existence of the KY tensors in the Taub-NUT geometry allows constructing some Dirac-type operators related to the hidden symmetry of the problem. On the other hand, the Dirac equation admits an analytic solution, and the energy levels are similar to those in the scalar mode case [8], [9].…”

“…In the above representation of the Dirac matrices, the Hamiltonian operator of the massless Dirac field is [7]- [9] H =γ 5 …”

Geodesic Motions in Euclidean Taub-NUT Spinning Spaces

“…Moreover, the motion of well-separated monopole-monopole interactions is described approximately by the geodesics of this space [30][31][32][33]. The Euclidean Taub-NUT background contains also interesting specific features of the quantum theory in the case of the scalar fields [34] as well as for Dirac fields of spin-1 2 fermions [35][36][37]. There exist large algebras of conserved observables in both cases [38].…”