Elements of symplectic covariant theory of phase-space Schrödinger equations
Résumé
We construct an irreducible representation of the Heisenberg group on Hilbert spaces of phase-space functions. This leads us to an extended Weyl calculus making possible a rigorous treatment of Schrödinger equations in phase space, justified by Stone-von neumann's theorem. We discuss the physical relevance and probabilistic interpretation of the solutions to this equation.