Symmetries and motions in manifolds
Feb, 199218 pages
Published in:
- J.Geom.Phys. 11 (1993) 559
Contribution to:
e-Print:
- hep-th/9205074 [hep-th]
Report number:
- NIKHEF-H-92-08
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Abstract:
Lectures at 28th Winter School of Theoretical Physics, Karpacz (Poland, 1992) by J.W. van Holten. Abstract: 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.References(11)
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