The Dirac point electron in zero-gravity Kerr–Newman spacetime

Dirac’s wave equation for a point electron in the topologically nontrivial maximal analytically extended electromagnetic Kerr–Newman spacetime is studied in a limit G → 0, where G is Newton’s constant of universal gravitation. The following results are obtained: the formal Dirac Hamiltonian on the s...

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Bibliographic Details
Published in:Journal of mathematical physics 2015-04, Vol.56 (4), p.1
Main Authors: Kiessling, M. K.-H., Tahvildar-Zadeh, A. S.
Format: Article
Language:English
Subjects:
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
Dipole moments
DIRAC OPERATORS
Electromagnetism
ELECTRONS
GRAVITATION
Gravity
HAMILTONIANS
MAGNETIC DIPOLE MOMENTS
Physics
Relativity
S waves
SPACE-TIME
Spacetime
Spectrum analysis
Symmetry
TOPOLOGY
Wave equations
WEIGHTLESSNESS
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Summary:Dirac’s wave equation for a point electron in the topologically nontrivial maximal analytically extended electromagnetic Kerr–Newman spacetime is studied in a limit G → 0, where G is Newton’s constant of universal gravitation. The following results are obtained: the formal Dirac Hamiltonian on the static spacelike slices is essentially self-adjoint and the spectrum of the self-adjoint extension is symmetric about zero, featuring a continuum with a gap about zero that, under two smallness conditions, contains a point spectrum. The symmetry result extends to the Dirac operator on a generalization of the zero-G Kerr–Newman spacetime with different electric-monopole/magnetic-dipole-moment ratios.
ISSN:0022-2488
1089-7658
DOI:10.1063/1.4918361