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Dynamical symmetries of the Geodesic equation

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Abstract

A class of dynamical symmetries for the Euler-Lagrange equations corresponding to the LagrangianL=(1/2)g ab q a q b is determined. The members of the class are closely related to tensor fields defined on the configuration space. First integrals generated by the dynamical symmetries through deformation of a given first integral are then examined. Noether-type conserved quantities whose expression depends only on the dynamical symmetry are also explicitly exhibited. Applications to general relativity are also pointed out in the course of the discussion.

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Authors and Affiliations

  1. Istituto Matematico dell'Università, via L. B. Alberti, 4, 16132, Genova, Italy

    Giacomo Caviglia

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  1. Giacomo Caviglia
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Work done under the auspices of the National Group for Mathematical Physics of C.N.R.

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Caviglia, G. Dynamical symmetries of the Geodesic equation. Int J Theor Phys 22, 1051–1065 (1983). https://doi.org/10.1007/BF02080551

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  • DOI: https://doi.org/10.1007/BF02080551

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