4 papers
A Phase Space Representation of the Metaplectic Group
Maurice de Gosson
The symplectic group Sp(n) acts on phase space while the unitary representation of its double cover, Mp(n), the metaplectic group, acts on functions defined on configuration space.…
Quantum Monads in Phase Space and Related Toeplitz Operators
Maurice de Gosson
In earlier work, we introduced quantum blobs as minimum-uncertainty symplectic ellipsoids in phase space. These objects may be viewed as geometric monads in the Leibnizian sense, r…
Polar Duality and the Donoho--Stark Uncertainty Principle
Maurice de Gosson
Polar duality is a fundamental geometric concept that can be interpreted as a form of Fourier transform between convex sets. Meanwhile, the Donoho-Stark uncertainty principle in ha…
Quantum Indeterminacy and Polar Duality: a Probabilistic Approach
Maurice de Gosson
We present a probabilistic argument supporting the application of polar duality, as discussed in our previous work, to express the indeterminacy principle of quantum mechanics. Our…