2000/08/23 by Ion I. Cotăescu, ION I. COTĂESCU, Mihai Visinescu +1 · 2 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Quantum Mechanics and Non-Hermitian Physics #gr-qc #hep-th
paper · pdf · doi:10.1142/s0217751x01003287
published as Int.J.Mod.Phys. A16 (2001) 1743-1758 · 20 pages, latex, no figures
arxiv created 2000/08/23 · openalex publication_date 2001/04/20 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
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 Schrödinger 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-Kähler Taub–NUT space. The energy eigenspinors of the central modes in spherical coordinates are completely evaluated in explicit, closed form.