74 research outputs found
Supersymmetries and constants of motion in Taub-NUT spinning space
We review the geodesic motion of pseudo-classical spinning particles in
curved spaces. Investigating the generalized Killing equations for spinning
spaces, we express the constants of motion in terms of Killing-Yano tensors.
The general results are applied to the case of the four-dimensional Euclidean
Taub-NUT spinning space. A simple exact solution, corresponding to trajectories
lying on a cone, is given.Comment: 33 pages, LaTeX2e, to appear in Fortschritte der Physi
Hidden Symmetries of Euclideanised Kerr-NUT-(A)dS Metrics in Certain Scaling Limits
The hidden symmetries of higher dimensional Kerr-NUT-(A)dS metrics are
investigated. In certain scaling limits these metrics are related to the
Einstein-Sasaki ones. The complete set of Killing-Yano tensors of the
Einstein-Sasaki spaces are presented. For this purpose the Killing forms of the
Calabi-Yau cone over the Einstein-Sasaki manifold are constructed. Two new
Killing forms on Einstein-Sasaki manifolds are identified associated with the
complex volume form of the cone manifolds. Finally the Killing forms on mixed
3-Sasaki manifolds are briefly described.Comment: 15 pages; text revised in Section 3.2, references adde
Covariant Approach of the Dynamics of Particles in External Gauge Fields, Killing Tensors and Quantum Gravitational Anomalies
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 St\"ackel-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.Comment: based on a talk at Symmetries and Integrability of Difference
Equations (SIDE-9), Varna, Bulgaria, June 201
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