The Dirac field in Taub-NUT background

Abstract

We investigate the SO(4,1) gauge-invariant theory of the Dirac fermions in the external field of the Kaluza-Klein monopole, pointing out that the quantum modes can be recovered from a Klein-Gordon equation analogous to the Schr\" odinger equation in the Taub-NUT background. Moreover, we show that there is a large collection of observables that can be directly derived from those of the scalar theory. These offer many possibilities of choosing complete sets of commuting operators which determine the quantum modes. In addition there are some spin- like and Dirac-type operators involving the covariantly constant Killing-Yano tensors of the hyper-K\" ahler Taub-NUT space. The energy eigenspinors of the central modes in spherical coordinates are completely evaluated in explicit, closed form.

20 pages, latex, no figures

References in corpus (3)

• Generalized Taub-NUT metrics and Killing-Yano tensors
• Schrödinger quantum modes on the Taub-NUT background
• The Dirac equation in Taub-NUT space

Cited by in corpus (8)

• Dynamical algebra and Dirac quantum modes in Taub-NUT background
• Fermions Tunneling from Plebanski-Demianski Black Holes
• Symmetries of the Dirac operators associated with covariantly constant Killing-Yano tensors
• Hierarchy of Dirac, Pauli and Klein-Gordon conserved operators in Taub-NUT background
• Infinite loop superalgebras of the Dirac theory on the Euclidean Taub-NUT space
• Superalgebras of Dirac operators on manifolds with special Killing-Yano tensors
• The induced representation of the isometry group of the Euclidean Taub-NUT space and new spherical harmonics
• Supersymmetry and discrete transformations of the Dirac operators in Taub-NUT geometry