Quantization of Singular Symplectic Quotients

2001
ISBN: 978-3-7643-6608-7
Verlag: Springer

Buch, Englisch, Band 198, 355 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 1540 g

Reihe: Progress in Mathematics

This is the first exposition of the quantization theory of singular symplectic (Marsden-Weinstein) quotients and their applications to physics. The reader will acquire an introduction to the various techniques used in this area, as well as an overview of the latest research approaches. These involve classical differential and algebraic geometry, as well as operator algebras and noncommutative geometry. Thus one will be amply prepared to follow future developments in this field.

Zielgruppe

Research

Autoren/Hrsg.

Landsman, N.P.

Pflaum, Markus

Schlichenmaier, Martin

Fachgebiete

• Mathematik | Informatik Mathematik Topologie Mengentheoretische Topologie
• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
• Mathematik | Informatik Mathematik Topologie Algebraische Topologie
• Mathematik | Informatik Mathematik Geometrie Elementare Geometrie: Allgemeines

Inhaltsverzeichnis

Some comments on the history, theory, and applicationsof symplectic reduction.- Homology of complete symbols and non-commutative geometry.- Cohomology of the Mumford quotient.- Poisson sigma models and symplectic groupoids.- Pseudo-differential operators and deformation quantization.- Singularities and Poisson geometry of certainrepresentation spaces.- Quantized reduction as a tensor product.- Analysis of geometric operator on open manifolds: a groupoid approach.- Smooth structures on stratified spaces.- Singular projective varieties and quantization.- Poisson structure and quantization of Chern-Simons theory.- Combinatorial quantization of Euclidean gravityin three dimensions.- The Yang—Mills measure and symplectic structureover spaces of connections.