The "Symplectic Camel Principle" and Semiclassical Mechanics

Details The "Symplectic Camel Principle" and Semiclassical Mechanics The "Symplectic Camel Principle" and Semiclassical Mechanics

2002-07-24

arxiv.org/abs/math/0207216v1

Mathematics

Symplectic Geometry

no figures. to appear in J. Phys. Math A. (2002)

Scientific paper

10.1088/0305-4470/35/32/305

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.

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