Dirac’s Point Electron in the Zero-Gravity Kerr–Newman World

Michael K.-H. Kiessling () and A. Shadi Tahvildar-Zadeh ()
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Michael K.-H. Kiessling: The State University of New Jersey, Department of Mathematics, Rutgers
A. Shadi Tahvildar-Zadeh: The State University of New Jersey, Department of Mathematics, Rutgers

A chapter in Quantum Mathematical Physics, 2016, pp 441-469 from Springer

Abstract: Abstract The results of a study of the Dirac Hamiltonian for a point electron in the zero-gravity Kerr–Newman spacetime are reported; here, “zero-gravity” means G → 0, where G is Newton’s constant of universal gravitation, and the limit is effected in the Boyer–Lindquist coordinate chart of the maximal analytically extended, topologically nontrivial, Kerr–Newman spacetime. In a nutshell, the results are: the essential self-adjointness of the Dirac Hamiltonian; the reflection symmetry about zero of its spectrum; the location of the essential spectrum, exhibiting a gap about zero; and (under two smallness assumptions on some parameters) the existence of a point spectrum in this gap, corresponding to bound states of Dirac’s point electron in the electromagnetic field of the zero-G Kerr–Newman ring singularity. The symmetry result of the spectrum extends to the Dirac Hamiltonian for a point electron in a generalization of the zero-G Kerr–Newman spacetime with different ratio of electric-monopole to magnetic-dipole moment. The results are discussed in the context of the general-relativistic hydrogen problem. Also, some interesting projects for further inquiry are listed in the lastsection.

Keywords: Kerr–Newman spacetime; Dirac electron; Zero-gravity limit (search for similar items in EconPapers)
Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-26902-3_19

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DOI: 10.1007/978-3-319-26902-3_19

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