First-order symmetries of Dirac equation in curved background: a unified dynamical symmetry condition

Abstract

It has been shown that, for all dimensions and signatures, the most general first-order linear symmetry operators for the Dirac equation including interaction with Maxwell field in curved background are given in terms of Killing-Yano (KY) forms. As a general gauge invariant condition it is found that among all KY-forms of the underlying (pseudo) Riemannian manifold, only those which Clifford commute with the Maxwell field take part in the symmetry operator. It is also proved that associated with each KY-form taking part in the symmetry operator, one can define a quadratic function of velocities which is a geodesic invariant as well as a constant of motion for the classical trajectory. Some geometrical and physical implications of the existence of KY-forms are also elucidated.

13 pages, put into sections and subsections format, added a conclusion part. Published version

References in corpus (4)

• Classification of the Weyl Tensor in Higher Dimensions and Applications
• `Hidden' Symmetries of Higher Dimensional Rotating Black Holes
• Higher-Dimensional Black Holes: Hidden Symmetries and Separation of Variables
• Conserved gravitational charges from Yano tensors

Cited by in corpus (20)

• Black holes, hidden symmetries, and complete integrability
• Hidden Symmetries of Dynamics in Classical and Quantum Physics
• Charged particle in higher dimensional weakly charged rotating black hole spacetime
• Commuting symmetry operators of the Dirac equation, Killing-Yano and Schouten-Nijenhuis brackets
• Symmetries of the Dirac operator with skew-symmetric torsion
• Hidden symmetry in the presence of fluxes
• Higher-degree Dirac Currents of Twistor and Killing Spinors in Supergravity Theories
• Basic Gravitational Currents and Killing-Yano Forms
• Symmetry operators of Killing spinors and superalgebras in AdS_5
• Spin raising and lowering operators for Rarita-Schwinger fields
• Gauged twistor spinors and symmetry operators
• Extended superalgebras from twistor and Killing spinors
• Second order symmetry operators for the massive Dirac equation
• Harmonic spinors from twistors and potential forms
• Killing-Yano Forms of a Class of Spherically Symmetric Space-Times II: A Unified Generation of Higher Forms
• On quantum numbers for Rarita-Schwinger fields
• Higher-dimensional lifts of Killing-Yano forms with torsion
• Spin-1/2 and spin-3/2 field solutions in plane wave spacetimes
• Symmetries of modified Dirac operators in supergravity flux backgrounds
• Algebra structure of conformal Killing-Yano forms in geometries with skew-symmetric torsion