Overview

In diesem Buch werden die Grundlagen der Poisson-Geometrie und der Deformationsquantisierung ausgehend von physikalischen Fragestellungen auf kohärente Weise entwickelt. Die Poisson-Geometrie bietet einen allgemeinen Rahmen für die geometrische Mechanik und stellt eine Verallgemeinerung der symplektischen Geometrie dar. Diese nimmt, insbesondere im Hinblick auf mechanische Systeme mit Symmetrien und deren Phasenraumreduktion, einen wichtigen Platz ein. Für die angestrebte Quantisierung werden die geometrischen Sachverhalte algebraisch gedeutet und entsprechend formuliert. Darauf aufbauend bietet die Deformationsquantisierung einen allgemeinen Rahmen für die Quantisierung von Poisson-Mannigfaltigkeiten, der nun erstmals in Lehrbuchform entwickelt wird. Zentrale Themen wie die Fedosov-Konstruktion von Sternprodukten sowie Elemente der Darstellungstheorie der deformierten Algebren werden im Detail vorgestellt. Ausführliche Beweise und über 100 Übungsaufgaben mit Lösungshinweisen erleichtern ein Selbststudium.

Full Product Details

Author:   Stefan Waldmann
Publisher:   Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint:   Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Dimensions:   Width: 15.50cm , Height: 3.60cm , Length: 23.50cm
Weight:   1.910kg
ISBN:  

9783540725176

ISBN 10:   3540725172
Pages:   612
Publication Date:   05 September 2007
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   In Print  
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Language:   German

Table of Contents

Aspekte der Hamiltonschen Mechanik.- Differentialgeometrische Grundlagen.- Symplektische Geometrie.- Poisson-Geometrie.- Quantisierung: Erste Schritte.- Formale Deformationsquantisierung.- Zustande und Darstellungen.

Reviews

From the reviews: The book under review provides a welcome unified exposition on Poisson geometry and deformation quantization. This book will certainly prove to be a useful introductory text for a very active research area where ideas of mathematical physics, differential geometry and operator theory are interacting. The exposition is clear and many comments with a physical flavor are included throughout the text. (Daniel Beltita, Zentralblatt MATH, Vol. 1139 (17), 2008) From the reviews: The book under review provides a welcome unified exposition on Poisson geometry and deformation quantization. ... This book will certainly prove to be a useful introductory text for a very active research area where ideas of mathematical physics, differential geometry and operator theory are interacting. The exposition is clear and many comments with a physical flavor are included throughout the text. (Daniel Beltita, Zentralblatt MATH, Vol. 1139 (17), 2008) From the reviews: The book under review provides a welcome unified exposition on Poisson geometry and deformation quantization. This book will certainly prove to be a useful introductory text for a very active research area where ideas of mathematical physics, differential geometry and operator theory are interacting. The exposition is clear and many comments with a physical flavor are included throughout the text. (Daniel Beltita, Zentralblatt MATH, Vol. 1139 (17), 2008) From the reviews: The book under review provides a welcome unified exposition on Poisson geometry and deformation quantization. This book will certainly prove to be a useful introductory text for a very active research area where ideas of mathematical physics, differential geometry and operator theory are interacting. The exposition is clear and many comments with a physical flavor are included throughout the text. (Daniel Beltita, Zentralblatt MATH, Vol. 1139 (17), 2008) From the reviews: The book under review provides a welcome unified exposition on Poisson geometry and deformation quantization. This book will certainly prove to be a useful introductory text for a very active research area where ideas of mathematical physics, differential geometry and operator theory are interacting. The exposition is clear and many comments with a physical flavor are included throughout the text. (Daniel Beltita, Zentralblatt MATH, Vol. 1139 (17), 2008)

From the reviews: </p> The book under review provides a welcome unified exposition on Poisson geometry and deformation quantization. This book will certainly prove to be a useful introductory text for a very active research area where ideas of mathematical physics, differential geometry and operator theory are interacting. The exposition is clear and many comments with a physical flavor are included throughout the text. (Daniel Beltita, Zentralblatt MATH, Vol. 1139 (17), 2008)</p>

From the reviews: The book under review provides a welcome unified exposition on Poisson geometry and deformation quantization. This book will certainly prove to be a useful introductory text for a very active research area where ideas of mathematical physics, differential geometry and operator theory are interacting. The exposition is clear and many comments with a physical flavor are included throughout the text. (Daniel Beltita, Zentralblatt MATH, Vol. 1139 (17), 2008)

<p>From the reviews: <p><p> The book under review provides a welcome unified exposition on Poisson geometry and deformation quantization. This book will certainly prove to be a useful introductory text for a very active research area where ideas of mathematical physics, differential geometry and operator theory are interacting. The exposition is clear and many comments with a physical flavor are included throughout the text. (Daniel Beltita, Zentralblatt MATH, Vol. 1139 (17), 2008)

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