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  - 
TY  - BOOK
A1  - Gosson, Maurice A. de
T1  - Symplectic geometry, wigner-weyl-moyal calculus, and quantum mechanics, in phase space ; Part 1
T3  - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell
Y1  - 2006
SN  - 1437-739X
PB  - Univ.
CY  - Potsdam
ER  - 
TY  - BOOK
A1  - Gosson, Maurice A. de
T1  - Symplectic geometry, wigner-weyl-moyal calculus, and quantum mechanics, in phase space ; Part 2
T3  - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell
Y1  - 2006
SN  - 1437-739X
PB  - Univ.
CY  - Potsdam
ER  - 
TY  - BOOK
A1  - Gosson, Maurice A. de
T1  - Symplectic geometry, wigner-weyl-moyal calculus, and quantum mechanics, in phase space ; Part 3
T3  - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell
Y1  - 2006
SN  - 1437-739X
PB  - Univ.
CY  - Potsdam
ER  - 
TY  - INPR
A1  - Gosson, Maurice A. de
T1  - Symplectic geometry, Wigner-Weyl-Moyal calculus, and quantum mechanics in phase space
N2  - Contents: Part I: Symplectic Geometry Chapter 1: Symplectic Spaces and Lagrangian Planes Chapter 2: The Symplectic Group Chapter 3: Multi-Oriented Symplectic Geometry Chapter 4: Intersection Indices in Lag(n) and Sp(n) Part II: Heisenberg Group, Weyl Calculus, and Metaplectic Representation Chapter 5: Lagrangian Manifolds and Quantization Chapter 6: Heisenberg Group and Weyl Operators Chapter 7: The Metaplectic Group Part III: Quantum Mechanics in Phase Space Chapter 8: The Uncertainty Principle Chapter 9: The Density Operator Chapter 10: A Phase Space Weyl Calculus
T3  - Preprint - (2006) 06 
Y1  - 2006
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-30212
ER  -