Letters in Mathematical Physics

, Volume 72, Issue 2, pp 129–142 | Cite as

On the Weyl Representation of Metaplectic Operators

Article

Abstract

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.

Keywords

Weyl symbol metaplectic operators Maslov and Conley–Zehnder index Gutzwiller formula 

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Copyright information

© Springer 2005

Authors and Affiliations

  1. 1.Institut für MathematikUniversität PotsdamPotsdamGermany

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