Abstract
The phase space of Hamiltonean systems is a symplectic manifold (M, ω). Let a Lie group G act on (M, ω) by symplectic automorphisms. The momen tum map 1) provides a geometric formulation of the relationship between symmetries and conserved quantities. It is a map
where g * is the dual of the Lie algebra g · of G, defined in the following way:
.
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References
A standard reference for Mechanics on symplectic manifolds is R. Abraham, J.E. Marsden: Foundations of Mechanics 2nd edition 1978 The Benjamin/Cummings Publishing Comp., Inc.
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Römer, H. (1988). Singular Points in Level Sets of the Momentum Map and Quantum Theory. In: Bleuler, K., Werner, M. (eds) Differential Geometrical Methods in Theoretical Physics. NATO ASI Series, vol 250. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-7809-7_16
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DOI: https://doi.org/10.1007/978-94-015-7809-7_16
Publisher Name: Springer, Dordrecht
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