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

Symmetry Integrability and Geometry-Methods and Applications

article

Mihai Visinescu¹ 

[1] Department of Theoretical Physics, National Institute for Physics and Nuclear Engineering

关键词: hidden symmetries;    Killing tensors;    Killing–Maxwell system;    quantum anomalies;   

DOI  :  10.3842/SIGMA.2011.037

来源: National Academy of Science of Ukraine

【 摘 要 】

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.

【 授权许可】

Unknown