Abstract
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 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. The formalism is applied to solve for the motion of a pseudo-classical electron in Schwarzschild space-time. (author). 15 refs.
Holten, J.W. van;
Rietdijk, R H
[1]
- Nationaal Inst. voor Kernfysica en Hoge-Energiefysica (NIKHEF), Amsterdam (Netherlands). Sectie H
Citation Formats
Holten, J.W. van, and Rietdijk, R H.
Symmetries and motions in manifolds.
Netherlands: N. p.,
1992.
Web.
Holten, J.W. van, & Rietdijk, R H.
Symmetries and motions in manifolds.
Netherlands.
Holten, J.W. van, and Rietdijk, R H.
1992.
"Symmetries and motions in manifolds."
Netherlands.
@misc{etde_10147431,
title = {Symmetries and motions in manifolds}
author = {Holten, J.W. van, and Rietdijk, R H}
abstractNote = {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 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. The formalism is applied to solve for the motion of a pseudo-classical electron in Schwarzschild space-time. (author). 15 refs.}
place = {Netherlands}
year = {1992}
month = {Dec}
}
title = {Symmetries and motions in manifolds}
author = {Holten, J.W. van, and Rietdijk, R H}
abstractNote = {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 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. The formalism is applied to solve for the motion of a pseudo-classical electron in Schwarzschild space-time. (author). 15 refs.}
place = {Netherlands}
year = {1992}
month = {Dec}
}