Symplectic Non-Squeezing Theorems, Quantization of Integrable Systems, and Quantum Uncertainty
Mathematical Physics
2007-05-23 v1 math.MP
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.
Cite
@article{arxiv.math-ph/0602055,
title = {Symplectic Non-Squeezing Theorems, Quantization of Integrable Systems, and Quantum Uncertainty},
author = {Maurice De Gosson},
journal= {arXiv preprint arXiv:math-ph/0602055},
year = {2007}
}