# Extension of the Conley-Zehnder index, a product formula, and an application to the Weyl representation of metaplectic operators

@article{Gosson2006ExtensionOT, title={Extension of the Conley-Zehnder index, a product formula, and an application to the Weyl representation of metaplectic operators}, author={Maurice A. de Gosson and Serge M. de Gosson}, journal={Journal of Mathematical Physics}, year={2006}, volume={47}, pages={123506-123506} }

The aim of this paper is to express the Conley-Zehnder index of a symplectic path in terms of an index due to Leray and which has been studied by one of us in a previous work. This will allow us to prove a formula for the Conley-Zehnder index of the product of two symplectic paths in terms of a symplectic Cayley transform. We apply our results to a rigorous study of the Weyl representation of metaplectic operators, which plays a crucial role in the understanding of semiclassical quantization of…

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