Generalized Killing equations for spinning spaces and the role of Killing-Yano tensors

The generalized Killing equations for the configuration space of spinning particles (spinning space) are analysed. Solutions of these equations are expressed in terms of Killing-Yano tensors. In general the constants of motion can be seen as extensions of those from the scalar case or new ones depending on the Grassmann-valued spin variables.Comment: LaTeX, 6 pages, Talk given at the International Symposium on the Theory of Elementary Particles, Buckow 199

On the Lattice Corrections to the Free Energy of Kink-Bearing Nonlinear One-Dimensional Scalar Systems

A ri proof of the effective potential (lattice corrections included) deduced by Trullinger and Sasaki is given. Using asymptotic methods from the theory of differential equations depending on a large parameter, the lattice corrections to the kink and kink-kink contributions to the free energy are calculated. The results are in complete agreement with a first order correction to the energy of the static kink.Comment: 12 pages,plainte

Hidden symmetries in a gauge covariant approach, Hamiltonian reduction and oxidation

Hidden symmetries in a covariant Hamiltonian formulation are investigated involving gauge covariant equations of motion. The special role of the Stackel-Killing tensors is pointed out. A reduction procedure is used to reduce the original phase space to another one in which the symmetries are divided out. The reverse of the reduction procedure is done by stages performing the unfolding of the gauge transformation followed by the Eisenhart lift in connection with scalar potentials.Comment: 15 pages; based on a talk at QTS-7 Conference, Prague, August 7-13, 201

Killing forms on the five-dimensional Einstein-Sasaki Y(p,q) spaces

We present the complete set of Killing-Yano tensors on the five-dimensional Einstein-Sasaki Y(p,q) spaces. Two new Killing-Yano tensors are identified, associated with the complex volume form of the Calabi-Yau metric cone. The corresponding hidden symmetries are not anomalous and the geodesic equations are superintegrable.Comment: 10 pages; improved versio

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