2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/74730We 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.To appear in Lett. Math. PhysiqueSymplectic GeometryMathematical PhysicsMSC: 81S30, 43A65, 43A32text