1. Symplectic spaces and Lagrangian planes -- 2. The symplectic group -- 3. Multi-oriented symplectic geometry -- 4. Intersection indices in Lag(n) and Sp(n) -- 5. Lagrangian manifolds and quantization -- 6. Heisenberg group and Weyl operators -- 7. The metaplectic group -- 8. The uncertainty principle -- 9. The density operator -- 10. A phase space Weyl calculus -- A. Classical Lie groups -- B. Covering spaces and groups -- C. Pseudo-differential operators -- D. Basics of probability theory
Summary
Focuses on the discussion of techniques and topics intervening in the mathematical treatment of quantum and semi-classical mechanics. This book starts with an introduction to symplectic geometry. It is of interest for mathematicians working in geometry and topology
Bibliography
Includes bibliographical references (pages 355-363) and index
