Geometric Quantization
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Geometric Quantization
Author: Nicholas Michael John Woodhouse
language: en
Publisher: Oxford University Press
Release Date: 1992
This book presents a survey of the geometric quantization theory of Kostant and Souriau and was first published in 1980. It has been extensively rewritten and brought up to date, with the addition of many new examples.
Loop Spaces, Characteristic Classes and Geometric Quantization
Author: Jean-Luc Brylinski
language: en
Publisher: Springer Science & Business Media
Release Date: 2009-12-30
This book examines the differential geometry of manifolds, loop spaces, line bundles and groupoids, and the relations of this geometry to mathematical physics. Applications presented in the book involve anomaly line bundles on loop spaces and anomaly functionals, central extensions of loop groups, Kähler geometry of the space of knots, and Cheeger--Chern--Simons secondary characteristics classes. It also covers the Dirac monopole and Dirac’s quantization of the electrical charge.
Geometric Quantization and Quantum Mechanics
Author: Jedrzej Sniatycki
language: en
Publisher: Springer Science & Business Media
Release Date: 2012-12-06
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.