On the Weyl Representation of Metaplectic OperatorsReport as inadecuate

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1 Institut für Mathematik Potsdam

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

Author: Maurice De Gosson -

Source: https://hal.archives-ouvertes.fr/


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