Now showing items 1-10 of 37
Nonnegative mixed states in Weyl–Wigner–Moyal theory
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.
On the kinematics of the last Wigner particle
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 ...
The chirality theorem
We show how chirality of the weak interactions stems from string independence in the string-local formalism of quantum field theory.
Quantum electrodynamics in external fields from the spin representation
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 ...
Distinguished Hamiltonian theorem for homogeneous symplectic manifolds
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 ...
Moyal quantization with compact symmetry groups and noncommutative harmonic analysis
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 ...
The metaplectic representation and boson fields
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's fine notion of divergent amplitudes
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 ...
Fourier analysis on the affine group, quantization and noncompact Connes geometries
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 ...
The Moyal representation of quantum mechanics and special function theory
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 ...