The "Symplectic Camel Principle" and Semiclassical Mechanics
Symplectic Geometry
2009-11-07 v1 Dynamical Systems
Abstract
Gromov's nonsqueezing theorem, aka the property of the symplectic camel, leads to a very simple semiclassical quantiuzation scheme by imposing that the only "physically admissible" semiclassical phase space states are those whose symplectic capacity (in a sense to be precised) is nh + (1/2)h where h is Planck's constant. We the construct semiclassical waveforms on Lagrangian submanifolds using the properties of the Leray-Maslov index, which allows us to define the argument of the square root of a de Rham form.
Cite
@article{arxiv.math/0207216,
title = {The "Symplectic Camel Principle" and Semiclassical Mechanics},
author = {Maurice de Gosson},
journal= {arXiv preprint arXiv:math/0207216},
year = {2009}
}
Comments
no figures. to appear in J. Phys. Math A. (2002)