Dynamical symmetries: An approach to Jacobi fields and to constants of geodesic motion
- 1 August 1983
- journal article
- research article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 24 (8) , 2065-2069
- https://doi.org/10.1063/1.525948
Abstract
It is shown that every dynamical symmetry (DS) of the Euler–Lagrange equations derived from the Lagrangian L =(1/2)gabq̇aq̇b identifies a Jacobi field on each geodesic of the configuration manifold. Using the connections between Jacobi fields and DS’s, it is proved that DS’s always possess associated conserved quantities, whose expression is explicitly written down. An additional constant of motion concomitant with ‘‘pairs’’ of DS’s, independently of the choice of L, is also determined. Applications to general relativity are emphasized in the course of the discussion.Keywords
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