Runge-Lenz operator for Dirac field in Taub-NUT background

Abstract

Fermions in D=4 self-dual Euclidean Taub-NUT space are investigated. Dirac-type operators involving Killing-Yano tensors of the Taub-NUT geometry are explicitly given showing that they anticommute with the standard Dirac operator and commute with the Hamiltonian as it is expected. They are connected with the hidden symmetries of the space allowing the construction of a conserved vector operator analogous to the Runge-Lenz vector of the Kepler problem. This operator is written down pointing out its algebraic properties.

10 pages, latex, no figures. Version to appear in Phys.Lett.B

References in corpus (2)

• Helicity supersymmetry of dyons
• The Dirac equation in Taub-NUT space

Cited by in corpus (11)

• Killing-Yano tensors and some applications
• Dirac Spinor Waves and Solitons in Anisotropic Taub-NUT Spaces
• Curved manifolds with conserved Runge-Lenz vectors
• Dynamical algebra and Dirac quantum modes in Taub-NUT background
• Particle in a self-dual dyon background: hidden free nature, and exotic superconformal symmetry
• 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
• Supersymmetry and discrete transformations of the Dirac operators in Taub-NUT geometry
• The induced representation of the isometry group of the Euclidean Taub-NUT space and new spherical harmonics
• The Dirac operator on generalized Taub-NUT spaces