2002/03/08 by Pedro de M. Rios, A. Ozorio de Almeida · 20 citations
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Geometric and Algebraic Topology #Hamilton–Jacobi equation #Homotopy and Cohomology in Algebraic Topology #Mathematical analysis #Mathematics #Pure mathematics #Simple (philosophy) #Symplectic geometry #Variational principle #math-ph #math.MP #math.SG
paper · pdf · doi:10.1016/j.geomphys.2003.12.001
published in Journal of Geometry and Physics 51(4), 404-441 (Elsevier BV) · 28 pages. Edited english translation of first author's PhD thesis (2000)
arxiv created 2002/03/08 · openalex publication_date 2004/01/30 · arxiv updated 2014/11/17 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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.