On the Weyl Representation of Metaplectic Operators

Maurice de Gosson (1)

1 Institut für Mathematik [Potsdam]

We study the Weyl representation of metaplectic operators associated to a symplectic matrix having no non-trivial fixed point, and justify a formula suggested in earlier work of Mehlig and Wilkinson. We give precise calculations of the associated Maslov-type indices; these indices intervene in a crucial way in Gutzwiller's formula of semiclassical mechanics, and are simply related to an index defined by Conley and Zehnder.

Mots clés: Weyl symbol; metaplectic operators; Maslov and Conley-Zehnder index; Gutzwiller formula

Domaines: Géométrie symplectique [math.SG]; Physique mathématique [math-ph]

Maurice de Gosson. On the Weyl Representation of Metaplectic Operators. 2005. ⟨hal-00004602⟩