Letters in Mathematical Physics

, Volume 72, Issue 2, pp 129–142

On the Weyl Representation of Metaplectic Operators

Article

DOI: 10.1007/s11005-005-4391-y

Cite this article as:
Gosson, M.A.D. Lett Math Phys (2005) 72: 129. doi:10.1007/s11005-005-4391-y

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 symbolmetaplectic operatorsMaslov and Conley–Zehnder indexGutzwiller formula

Copyright information

© Springer 2005

Authors and Affiliations

  1. 1.Institut für MathematikUniversität PotsdamPotsdamGermany