The Dirac field in Taub-NUT background

Details The Dirac field in Taub-NUT background The Dirac field in Taub-NUT background

2000-08-23

arxiv.org/abs/hep-th/0008181v1

Int.J.Mod.Phys. A16 (2001) 1743-1758

Physics

High Energy Physics

High Energy Physics - Theory

20 pages, latex, no figures

Scientific paper

10.1142/S0217751X01003287

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.

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