Higher order symmetries on curved spaces: gauge covariant approach and gravitational anomalies

Anca Visinescu, Mihai Visinescu

The higher order symmetries are investigated in a covariant Hamiltonian formulation. The covariant phase-space approach is extended to include the presence of external gauge fields and scalar potentials. The special role of the Killing-Yano tensors is pointed out. Some non-trivial examples involving Runge-Lenz type conserved quantities are explicitly worked out. The relationship between hidden symmetries in a curved space background and the corresponding quantum operators that commute with the fundamental wave operator in a first-quantized field theory is investigated. It is shown that the conformal Killing tensors do not in general produce symmetry operators for the Klein-Gordon equation. In the case of the standard Killing tensors under a few notable favorable circumstances the existence of such operators is possible. However conformal Killing tensors are sources of gravitational anomalies even if they are square of conformal Killing-Yano tensors.

References
[1] M. Visinescu, Mod. Phys. Lett. A 25, 341 (2010)
[2] S. Ianus, M. Visinescu, G. E. Vilcu, SIGMA 5, 022 (2009).
[3] M. Visinescu, Europhys. Lett., 90, 41002 (2010).
[4] A. Visinescu, M. Visinescu, in preparation