Symplectic Non-Squeezing Theorems, Quantization of Integrable Systems, and Quantum Uncertainty

2006/02/22 by Maurice De Gosson, De Gosson, Maurice
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Mathematical Physics (math-ph) #NA #math-ph #math.MP

paper · pdf · doi:10.48550/arxiv.math-ph/0602055

arxiv created 2006/02/22 · arxiv updated 2009/12/01

Abstract

The ground energy level of an oscillator cannot be zero because of Heisenberg's uncertainty principle. We use methods from symplectic topology (Gromov's non-squeezing theorem, and the existence of symplectic capacities) to analyze and extend this heuristic observation to Liouville-integrable systems, and to propose a topological quantization scheme for such systems, thus extending previous results of ours.

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