Symplectic Geometry And Quantization
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Symplectic Geometry and Mathematical Physics
The proceedings of a June 1990 conference in Aix-en-Provence, France, containing 22 papers (of which seven are in French). Many include findings that will not be published elsewhere, in such areas of geometric quantization as Poisson manifolds, simplectic geometry, classical mechanics, and particles and fields in physics. No subject index. Annotation copyrighted by Book News, Inc., Portland, OR
Symplectic Geometry and Quantum Mechanics
Author: Maurice A. de Gosson
language: en
Publisher: Springer Science & Business Media
Release Date: 2006-08-06
This book offers a complete discussion of techniques and topics intervening in the mathematical treatment of quantum and semi-classical mechanics. It starts with a very readable introduction to symplectic geometry. Many topics are also of genuine interest for pure mathematicians working in geometry and topology.
Lectures on the Geometry of Quantization
These notes are based on a course entitled ``Symplectic Geometry and Geometric Quantization'' taught by Alan Weinstein at the University of California, Berkeley (fall 1992) and at the Centre Emile Borel (spring 1994). The only prerequisite for the course needed is a knowledge of the basic notions from the theory of differentiable manifolds (differential forms, vector fields, transversality, etc.). The aim is to give students an introduction to the ideas of microlocal analysis and the related symplectic geometry, with an emphasis on the role these ideas play in formalizing the transition between the mathematics of classical dynamics (hamiltonian flows on symplectic manifolds) and quantum mechanics (unitary flows on Hilbert spaces). These notes are meant to function as a guide to the literature. The authors refer to other sources for many details that are omitted and can be bypassed on a first reading.