TY  - JOUR
A1  - Gosson, Maurice A. de
A1  - Gosson, Serge M. de
T1  - Extension of the Conley-Zehnder index, a product formula, and an application to the Weyl representation of metaplectic operators
JF  - Journal of mathematical physics
N2  - 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 Hamiltonian systems exhibiting chaotic behavior.
Y1  - 2006
U6  - https://doi.org/10.1063/1.239066
SN  - 0022-2488
VL  - 47
IS  - 12
PB  - American Institute of Physics
CY  - Melville
ER  -