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

Journal Article · Fri Dec 15 00:00:00 EST 2006 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.2390661· OSTI ID:20861565

Gosson, Maurice A. de; Gosson, Serge M. de ^[1]

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1. Institut fuer Mathematik, Universitaet Potsdam, Am Neuen Palais 10, D-14415 Potsdam (Germany)

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.

• OSTI ID: 20861565
• Journal Information: Journal of Mathematical Physics, Vol. 47, Issue 12; Other Information: DOI: 10.1063/1.2390661; (c) 2006 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
CHAOS THEORY
GROUP THEORY
HAMILTONIANS
QUANTIZATION
SEMICLASSICAL APPROXIMATION