Geometric quantization

Geometric quantization by Nicholas Woodhouse Download PDF EPUB FB2

The geometric approach to quantization was introduced by Konstant and Souriau more than 20 years ago. It has given valuable and lasting insights into the relationship between classical and quantum systems, and continues to be a popular research topic.

The ideas have proved useful in pure mathematics, notably in representation theory, as well as 4/5(1).

7 Geometric Quantization 93 a geometric viewpoint, is [41]. The book [29] treats further topics in symplectic geometry turn provides a geometric foundation for the further analysis of this and other formulations of quantum mechanics. These notes are still not in final form, but they have already benefitted from the comments.

Full Description: "This book contains a revised and expanded version of the lecture notes of two seminar series given during the academic year /77 at the Department of Mathematics and Statistics of the University of Calgary, and in the summer of at the Institute of Theoretical Physics of the Technical University Clausthal.

The aim of the seminars was to present. The geometric approach to quantization was introduced by Konstant and Souriau more than 20 years ago.

It has given valuable and lasting insights into the relationship between classical and quantum systems, and continues to be a popular research topic. The ideas have proved useful in pure mathematics, notably in representation theory, as well as in theoretical physics. The books of Souriau () and Simms and Woodhouse () 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 by: An Invitation to Geometric Quantization Alex Fok Department of Mathematics, Cornell University April What is quantization.

Quantization is a process of associating a classical mechanical system to a Hilbert space. Through this process, classical observables are. This book presents a survey of the geometric quantization theory of Kostant and Souriau and was first published in It has been extensively rewritten and brought up to date, with the addition of many new examples.

Abstract. This chapter describes geometric quantization. The motivation for this mathematical is to mimic quantum mechanics, where a manifold (the “classical phase space”, parametrizing position and momentum) is replaced by a vector space with an inner product; in other words, a Hilbert space (the “space of wave functions”).

Geometric quantization. Given a prequantum bundle as above, the actual step of genuine geometric quantization consists first of forming half its space of sections in a certain sense.

Physically this means passing to the space of wavefunctions that depend only on canonical coordinates but not on canonicalsubgroups of the group of (exponentiated). The geometric approach to quantization was introduced by Konstant and Souriau more than 20 years ago.

It has given valuable and lasting insights into the relationship between classical and quantum systems, and continues to be a popular research topic. Approach your problems from the right It isn't that they can't see the solution. It end and begin with the answers. Then, is that they can't see the problem.

one day, perhaps you will fmd the final question. Chesterton, The Scandal of Father Brown 'The Point of a Pin'. 'The Hermit Clad in Crane Feathers' in R.

Van Gulik's The Chinese Maze Murders. GEOMETRIC QUANTIZATION OF CHERN SIMONS GAUGE THEORY are associated with the Jones polynomial, from the point of view of the three dimensional quantum field theory. Canonica l quantization. The goal is to associate a Hubert space to ev ery closed oriented 2 manifold Σ by canonical quantization of the Chern Simons theory on Σ x R.

As a. In mathematical physics, geometric quantization is a mathematical approach to defining a quantum theory corresponding to a given classical theory. It attempts to carry out quantization, for which there is in general no exact recipe, in such a way that certain analogies between the classical theory and the quantum theory remain manifest.

A discussion of the relation between geometric quantization and the Marsden—Weinstein reduction is presented in Chapter 9. The final chapter considers extending the theory of geometric quantization to Poisson manifolds, via the theory of symplectic : $ Lectures on Geometric Quantization.

Authors; D. Simms; N. Woodhouse; Book. 6 Citations; k Downloads; Part of the Lecture Notes in Physics book series (LNP, volume 53) Chapters Table of contents (9 chapters) About About this book; Table of contents.

Search within book. Front Matter. PDF. Introduction. Pages Then we can try to apply geometric quantization, or some generalization of it which also applies to Poisson manifolds. Let C 0 (g *) C_0(g^*) be a space of functions on g * g^* that go to 0 at infinity in a sufficiently nice way.

The quantization process should send this commutative algebra to some possibly non-commutative algebra. C 0 (g. Find many great new & used options and get the best deals for Oxford Mathematical Monographs: Geometric Quantization by N.

Woodhouse (, UK-Paperback, Reprint) at the best online prices at eBay. Free shipping for many products. The books of Souriau () and Simms and Woodhouse () 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.

Geometric Quantization 1 Introduction The aim of the geometric quantization program is to describe a quantization procedure in terms of natural geometric structures. To date, this program has succeeded in unifying various older meth-ods of quantizing finite dimensional physical systems.

The generalization to infinite-dimensional. In the second paper you'll find the geometric quantization of the harmonic oscillator with the Maslov correction. That example is not in the book. I think that that is all what geometric quantization achieves completely, in accordance with physics experiments and results.

If you read these two texts you'll know as much as you can hope in the field. Approach your problems from the right It isn't that they can't see the solution. It end and begin with the answers. Then, is that they can't see the problem.

one day, perhaps you will fmd the final question. G. K. Chesterton, The Scandal of Father Brown 'The Point of a Brand: Springer Netherlands.Geometric Quantization and Quantum Mechanics Jȩdrzej Śniatycki (auth.) This book contains a revised and expanded version of the lecture notes of two seminar series given during the academic year /77 at the Department of Mathematics and Statistics of the University of Calgary, and in the summer of at the Institute of Theoretical.GEOMETRIC QUANTIZATION 1.

The basic idea The setting of the Hamiltonian version of classical (Newtonian) mechanics is the phase space (position and momentum), which is a symplectic manifold.

The typical example of this is the cotangent bundle of a manifold. The manifold is the con guration space (ie setFile Size: KB.