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A variational principle for actions on symmetric symplectic spaces

Pedro de M. Rios·A. Ozorio de Almeida
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Abstract

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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Pedro de M. Rios, A. Ozorio de Almeida. 2002-03-08. A variational principle for actions on symmetric symplectic spaces. https://doi.org/10.1016/j.geomphys.2003.12.001

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