Abstract
Using the formalism of symplectic group actions and coadjoint orbits, we give a complete list of all classical simple Lie algebras which are local symmetries for a given Hamiltonian vector field.
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References
Lie, S., Theorie der Transformationsgruppen I, II, III, Chelsea Publ., New York, 1970.
Eisenhart, L.P., Continuous Groups of Transformations, Princeton Univ. Press, Princeton, New Jersey, 1933.
Rosen, J., Nuovo Cimento 49A, 614 (1967).
Mukunda, N., J. Math. Phys. 8, 1069 (1967).
Caratu, G., Marmo, G., Simoni, A., Vitale, B., and Zaccharia, F., Nuovo Cimento 19B, 228 (1974).
Wolf, J.A., ‘Representations Associated to Minimal Coadjoint Orbits’, in Lect. Notes in Math. 676, Springer, New York, 1970.
Souriau, J.-M., Structure des Systèmes Dynamiques, Dunod, Paris, 1970.
Abraham, R. and Marsden, J., Foundations of Mechanics, Benjamin, Reading, Massachusetts, 1978.
Robbin, J.W., ‘Symplectic Mechanics’, in Global Analysis and its Applications III, IAEA, Vienna, 1974.
Palais, R.S., ‘A Global Formulation of the Lie Theory of Transformation Groups’, Mem. Am. Math. Soc. 22 (1957).
Helgason, S., Differential Geometry, Lie Groups and Symmetric Spaces, Academic Press, New York, 1978.
Fradkin, D.M., Progr. Theoret. Phys. 37, 798 (1967).
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Aguirre, E., Doebner, H.D. & Hennig, J.D. All local classical symmetries in Hamiltonian mechanics. Lett Math Phys 7, 85–90 (1983). https://doi.org/10.1007/BF00398716
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DOI: https://doi.org/10.1007/BF00398716