On the Weyl Representation of Metaplectic Operators

Details On the Weyl Representation of Metaplectic Operators On the Weyl Representation of Metaplectic Operators

2005-03-30

arxiv.org/abs/math/0503708v1

Mathematics

Symplectic Geometry

To appear in Lett. Math. Physique

Scientific paper

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.

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