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

SUSY in the sky

Spinning particles in curved space-time can have fermionic symmetries generated by the square root of bosonic constants of motion other than the Hamiltonian. We present a general analysis of the conditions under which such new supersymmetries appear, and discuss the Poisson-Dirac algebra of the resulting set of charges, including the conditions of closure of the new algebra. An example of a new non-trivial supersymmetry is found in black-hole solutions of the Kerr-Newman type and corresponds to the Killing-Yano tensor, which plays an important role in solving the Dirac equation in these black-hole metrics.Comment: 28, NIKHEF-H/93-04 and DAMTP R92/4

Killing tensors and a new geometric duality

We present a theorem describing a dual relation between the local geometry of a space admitting a symmetric second-rank Killing tensor, and the local geometry of a space with a metric specified by this Killing tensor. The relation can be generalized to spinning spaces, but only at the expense of introducing torsion. This introduces new supersymmetries in their geometry. Interesting examples in four dimensions include the Kerr-Newman metric of spinning black-holes and self-dual Taub-NUT.Comment: 20 pages (a4), standard LaTeX, no figure

The Onset of Chaos in Spinning Particle Models

The onset of chaos in one-dimensional spinning particle models derived from pseudoclassical mechanical hamiltonians with a bosonic Duffing potential is examined. Using the Melnikov method, we indicate the presence of homoclinic entanglements in models with general potentials for the spins, and thus show that chaotic motions occur in these models.Comment: 9 pages in Revtex4 style, 4 figures (eps files

Ethnic Employees’ Behaviour Vis-a-Vis Customers in the Service Sector

Our age is the age of migration. The socio-economic position of ethnic groups in a globally mobile society has extensively been studied in recent years, from the perspective of their skills, language abilities, adjustment behaviour, and so forth. This study investigates the social and economic performance of ethnic groups in cities by addressing the question whether these groups have a higher or lower reputation or esteem on the labour market than their indigenous equals, seen from the perspective of the customer’s perception and satisfaction. There is a popular feeling that ethnic employees in the service sector are less client-centered than indigenous employees. Sometimes, stigmatization is mentioned as a factor that acts as a negative predictor for someone’s position on the job market. This phenomenon calls for a careful and critical assessment, as it may also rest on an unjustified stigma. Therefore, it is an interesting research question whether workers of ethnic origin, e.g., in the service sector are more or less client-friendly than others. How do others judge their social or economic performance? After an extensive literature review, we formulate several hypotheses on the actual behaviour of ethnic employees and test these on the basis of empirical fieldwork in the service sector – notably in the retail sector – in the city of Amsterdam. Our conclusion is that in general there is no ethnic bias in the behaviour of these employees, although our findings suggest that gender bias does occur.

Symmetries and Motions in Manifolds

In these lectures the relations between symmetries, Lie algebras, Killing vectors and Noether's theorem are reviewed. A generalisation of the basic ideas to include velocity-dependend co-ordinate transformations naturally leads to the concept of Killing tensors. Via their Poisson brackets these tensors generate an {\em a priori} infinite-dimensional Lie algebra. The nature of such infinite algebras is clarified using the example of flat space-time. Next the formalism is extended to spinning space, which in addition to the standard real co-ordinates is parametrized also by Grassmann-valued vector variables. The equations for extremal trajectories (`geodesics') of these spaces describe the pseudo-classical mechanics of a Dirac fermion. We apply the formalism to solve for the motion of a pseudo-classical electron in Schwarzschild space-time.Comment: 19 pages. Lectures at 28th Winter School of Theoretical Physics, Karpacz (Poland, 1992) by J.W. van Holte