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The Symplectic Camel and Quantum Universal Invariants: The Angel of Geometry versus the Demon of Algebra
2014
Quantum Matter
A positive de...nite symmetric matrix quali...es as a quantum mechanical covariance matrix if and only if + 1 2 i~ 0 where is the standard symplectic matrix. This well-known condition is a strong version of the uncertainty principle, which can be reinterpreted in terms of the topological notion of symplectic capacity, closely related to Gromov's non-squeezing theorem. We show that a recent re...nement of the latter leads to a new class of geometric invariants. These are the volumes of the
doi:10.1166/qm.2014.1111
fatcat:kauvu4zhxrefxdczfowwo2ocna