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On the Weyl Representation of Metaplectic Operators

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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.

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  1. Institut für Mathematik, Universität Potsdam, Am Neuen Palais 10, D-14415, Potsdam, Germany

    Maurice A. De. Gosson

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  1. Maurice A. De. Gosson
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Correspondence to Maurice A. De. Gosson.

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Gosson, M.A.D. On the Weyl Representation of Metaplectic Operators. Lett Math Phys 72, 129–142 (2005). https://doi.org/10.1007/s11005-005-4391-y

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  • DOI: https://doi.org/10.1007/s11005-005-4391-y

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