Geometric Quantization and Quantum Mechanics

Jȩdrzej Śniatycki (auth.)9780387904696, 0-387-90469-7, 3-540-90469-7

This book contains a revised and expanded version of the lecture notes of two seminar series given during the academic year 1976/77 at the Department of Mathematics and Statistics of the University of Calgary, and in the summer of 1978 at the Institute of Theoretical Physics of the Technical University Clausthal. The aim of the seminars was to present geometric quantization from the point of view· of its applica­ tions to quantum mechanics, and to introduce the quantum dynamics of various physical systems as the result of the geometric quantization of the classical dynamics of these systems. The group representation aspects of geometric quantiza­ tion as well as proofs of the existence and the uniqueness of the introduced structures can be found in the expository papers of Blattner, Kostant, Sternberg and Wolf, and also in the references quoted in these papers. The books of Souriau (1970) and Simms and Woodhouse (1976) present the theory of geometric quantization and its relationship to quantum mech­ anics. The purpose of the present book is to complement the preceding ones by including new developments of the theory and emphasizing the computations leading to results in quantum mechanics.

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Table of contents :
Front Matter….Pages i-ix
Introduction….Pages 1-37
Hamiltonian Dynamics….Pages 38-50
Prequantization….Pages 51-59
Representation Space….Pages 60-76
Blattner-Kostant-Sternberg Kernels….Pages 77-100
Quantization….Pages 101-113
Schrödinger Representation….Pages 114-141
Other Representations….Pages 142-159
Time-Dependent Schrödinger Equation….Pages 160-167
Relativistic Dynamics in an Electromagnetic Field….Pages 168-197
Pauli Representation for Spin….Pages 198-213
Back Matter….Pages 214-231