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The "Symplectic Camel Principle" and Semiclassical Mechanics

Maurice de Gosson
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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.

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Maurice de Gosson. 2002-07-24. The "Symplectic Camel Principle" and Semiclassical Mechanics. https://doi.org/10.1088/0305-4470%2F35%2F32%2F305

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