Displaying similar documents to “An algebra of pseudo-differential operators and quantum mechanics in phase space”

A mathematical introduction to the Wigner formulation of quantum mechanics

Luigi Barletti (2003)

Bollettino dell'Unione Matematica Italiana


The paper is devoted to review, from a mathematical point of view, some fundamental aspects of the Wigner formulation of quantum mechanics. Starting from the axioms of quantum mechanics and of quantum statistics, we justify the introduction of the Wigner transform and eventually deduce the Wigner equation.

Canonical commutation relations and interacting Fock spaces

Zied Ammari (2004)

Journées Équations aux dérivées partielles


We introduce by means of reproducing kernel theory and decomposition in orthogonal polynomials canonical correspondences between an interacting Fock space a reproducing kernel Hilbert space and a square integrable functions space w.r.t. a cylindrical measure. Using this correspondences we investigate the structure of the infinite dimensional canonical commutation relations. In particular we construct test functions spaces, distributions spaces and a quantization map which generalized...