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A Product Formula for the Conley-Zehnder Index; Application to the Weyl Representation of Metaplectic Operators

The aim of this paper is to prove a formula for the Conley-Zehnder index of the product of two symplectic paths in terms of a symplectic Cayley transform, and to apply this formula to the Weyl representation of metaplectic operators. Our derivation makes use of the properties of the extended Leray index studied in previous work.