Covariant Approach of the Dynamics of Particles in External Gauge Fields, Killing Tensors and Quantum Gravitational Anomalies

Abstract

We give an overview of the first integrals of motion of particles in the presence of external gauge fields in a covariant Hamiltonian approach. The special role of Stäckel-Killing and Killing-Yano tensors is pointed out. Some nontrivial examples involving Runge-Lenz type conserved quantities are explicitly worked out. A condition of the electromagnetic field to maintain the hidden symmetry of the system is stated. A concrete realization of this condition is given by the Killing-Maxwell system and exemplified with the Kerr metric. Quantum symmetry operators for the Klein-Gordon and Dirac equations are constructed from Killing tensors. The transfer of the classical conserved quantities to the quantum mechanical level is analyzed in connection with quantum anomalies.

based on a talk at Symmetries and Integrability of Difference Equations (SIDE-9), Varna, Bulgaria, June 2010

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• Generalized hidden symmetries and the Kerr-Sen black hole
• Covariant hamiltonian dynamics
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Cited by in corpus (1)

• Conformal Killing Tensors and covariant Hamiltonian Dynamics