A Weyl Calculus on Symplectic Phase Space

Maurice A. de Gosson (1, 2)

1 University of Potsdam = Universität Potsdam
2 Departamento de Matematica

We study the twisted Weyl symbol of metaplectic operators; this requires the definition of an index for symplectic paths related to the Conley-Zehnder index. We thereafter define a metaplectically covariant algebra of pseudo-differential operators acting on functions on symplectic space.

Mots clés: symplectic; Weyl calculus; Heisenberg group; metaplectic representation; Conley-Zehnder index; Maslov index

Domaines: Physique mathématique [math-ph]; Géométrie symplectique [math.SG]; Théorie des représentations [math.RT]; Algèbres d'opérateurs [math.OA]

Maurice A. de Gosson. A Weyl Calculus on Symplectic Phase Space. 2006. ⟨hal-00007947v2⟩