Symplectic Microgeometry II: Generating functions
Symplectic Geometry
2020-03-13 v2 Mathematical Physics
math.MP
Abstract
We adapt the notion of generating functions for lagrangian submanifolds to symplectic microgeometry. We show that a symplectic micromorphism always admits a global generating function. As an application, we describe hamiltonian flows as special symplectic micromorphisms whose local generating functions are the solutions of Hamilton-Jacobi equations. We obtain a purely categorical formulation of the temporal evolution in classical mechanics.
Cite
@article{arxiv.1103.0672,
title = {Symplectic Microgeometry II: Generating functions},
author = {Alberto S. Cattaneo and Benoit Dherin and Alan Weinstein},
journal= {arXiv preprint arXiv:1103.0672},
year = {2020}
}
Comments
27 pages, 1 figure