A variational principle for actions on symmetric symplectic spaces

Details A variational principle for actions on symmetric symplectic spaces A variational principle for actions on symmetric symplectic spaces

2002-03-08

arxiv.org/abs/math-ph/0203012v1

Physics

Mathematical Physics

28 pages. Edited english translation of first author's PhD thesis (2000)

Scientific paper

We present a definition of generating functions of canonical relations, which are real functions on symmetric symplectic spaces, discussing some conditions for the presence of caustics. We show how the actions compose by a neat geometrical formula and are connected to the hamiltonians via a geometrically simple variational principle which determines the classical trajectories, discussing the temporal evolution of such ``extended hamiltonians'' in terms of Hamilton-Jacobi-type equations. Simplest spaces are treated explicitly.

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