Abstract
We define affine transport lifts on the tangent bundle by associating a transport rule for tangent vectors with a vector field on the base manifold. Our aim is to develop tools for the study of kinetic/dynamic symmetries in particle motion. The new lift unifies and generalizes all the various existing lifted vector fields, with clear geometric interpretations. In particular, this includes the important but little-known “matter symmetries” of relativistic kinetic theory. We find the affine dynamical symmetries of general relativistic charged particle motion, and we compare this to previous results and to the alternative concept of “matter symmetry.”
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References
Berezdivin, R., and Sachs, R. K. (1973).Journal of Mathematical Physics,14, 1254.
Crampin, M. (1983).Journal of Physics A,16, 3755.
Crampin, M., and Pirani, F. A. E. (1986).Applicable Differential Geometry, Cambridge University Press, Cambridge.
Eisenhart, L. P. (1961).Continuous Groups of Transformations, Dover, New York.
Iwai, T. (1977).Tensor N.S.,31, 98.
Katzin, G. H., and Levine, J. (1974).Journal of Mathematical Physics,15, 1460.
Maartens, R., and Maharaj, S. D. (1985).Journal of Mathematical Physics,26, 2869.
Maartens, R., and Taylor, D. R. (in preparation).
Oliver, D. R., and Davis, W. R. (1979).Annals de l'Institut Henri Poincaré,30, 339.
Prince, G. E., and Crampin, M. (1984).General Relativity and Gravitation,16, 921, 1063.
Stephani, H. (1982).General Relativity, Cambridge University Press, Cambridge.
Yano, K., and Ishihara, S. (1973).Tangent and Cotangent Bundles, Marcel Dekker, New York.
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Maartens, R., Taylor, D.R. Lifted transformations on the tangent bundle, and symmetries of particle motion. Int J Theor Phys 32, 143–158 (1993). https://doi.org/10.1007/BF00674402
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DOI: https://doi.org/10.1007/BF00674402