Hamiltonian Reduction by Stages

2007
ISBN: 978-3-540-72469-8
Verlag: Springer Berlin Heidelberg

Buch, Englisch, Band 1913, 524 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 814 g

Reihe: Lecture Notes in Mathematics

In this volume readers will find for the first time a detailed account of the theory of symplectic reduction by stages, along with numerous illustrations of the theory. Special emphasis is given to group extensions, including a detailed discussion of the Euclidean group, the oscillator group, the Bott-Virasoro group and other groups of matrices. Ample background theory on symplectic reduction and cotangent bundle reduction in particular is provided. Novel features of the book are the inclusion of a systematic treatment of the cotangent bundle case, including the identification of cocycles with magnetic terms, as well as the general theory of singular reduction by stages.

Zielgruppe

Research

Autoren/Hrsg.

Marsden, Jerrold E.

Misiolek, Gerard

Ratiu, Tudor S.

Ortega, Juan-Pablo

Perlmutter, Matthew

Fachgebiete

• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
• Mathematik | Informatik Mathematik Geometrie Nicht-Euklidische Geometrie
• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Naturwissenschaften Physik Angewandte Physik Statistische Physik, Dynamische Systeme

Inhaltsverzeichnis

Background and the Problem Setting.- Symplectic Reduction.- Cotangent Bundle Reduction.- The Problem Setting.- Regular Symplectic Reduction by Stages.- Commuting Reduction and Semidirect Product Theory.- Regular Reduction by Stages.- Group Extensions and the Stages Hypothesis.- Magnetic Cotangent Bundle Reduction.- Stages and Coadjoint Orbits of Central Extensions.- Examples.- Stages and Semidirect Products with Cocycles.- Reduction by Stages via Symplectic Distributions.- Reduction by Stages with Topological Conditions.- Optimal Reduction and Singular Reduction by Stages, by Juan-Pablo Ortega.- The Optimal Momentum Map and Point Reduction.- Optimal Orbit Reduction.- Optimal Reduction by Stages.