A variational principle for actions on symmetric symplectic spaces
Mathematical Physics
2014-11-17 v1 math.MP
Symplectic Geometry
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.
Cite
@article{arxiv.math-ph/0203012,
title = {A variational principle for actions on symmetric symplectic spaces},
author = {Pedro de M. Rios and A. Ozorio de Almeida},
journal= {arXiv preprint arXiv:math-ph/0203012},
year = {2014}
}
Comments
28 pages. Edited english translation of first author's PhD thesis (2000)