The Weyl Representation of Metaplectic Operators and the Conley-Zehnder Index
Maurice de Gosson
given at strobl07 (21.06.07 16:15)
The metalectic group plays a´n important role in time-frequency analysis, in quantum mechanics, and in representation theory. We identify the Weyl symbol of metaplectic operatorsusing the notion of symplectic Cayley transform, and show that the correct phase is obtained by using the Conley-Zehnder index familiar from the theory of periodic Hamiltonian orbits.