We classify the gaussian Wigner functions corresponding to mixed states and show that, unlike the case of pure states, not all nonnegative mixed states are gaussian.

Wigner's particle classification provides for "continuous spin" representations of the Poincaré group, corresponding to a class of (as yet unobserved) massless particles. Rather than building their induced realizations by ...

We show how chirality of the weak interactions stems from string independence in the string-local formalism of quantum field theory.

Systematic use of the infinite-dimensional spin representation simplifies and rigorizes several questions in quantum field theory. This representation permutes "Gaussian" elements in the fermion Fock space, and is necessarily ...

A diffeomorphism of a finite-dimensional flat symplectic manifold which is canonoid with respect to all linear and quadratic Hamiltonians preserves the symplectic structure up to a factor: so runs the "quadratic Hamiltonian ...

The phase-space approach to quantization of systems whose symmetry group is compact and semisimple is developed from two basic principles: covariance and traciality. This generalizes results and methods already implemented ...

We construct explicitly the infinite-dimensional metaplectic representation and show how its use simplifies and rigorizes several questions in bosonic Quantum Field Theory. The representation permutes Gaussian elements in ...

Stora and coworkers refined the notion of divergent quantum amplitude, somewhat upsetting the standard power-counting recipe. This unexpectedly clears the way to new prototypes for free and interacting field theories of ...

We find the Stratonovich-Weyl quantizer for the nonunimodular affine group of the line. A noncommutative product of functions on the half-plane, underlying a noncompact spectral triple in the sense of Connes, is obtained ...

It is shown that the phase-space formulation of quantum mechanics is a rich source of special function identities. The Moyal formalism is reviewed for two phase spaces: the real plane and the sphere; and this is used to ...