Overview
- Provides profound yet compact knowledge in manifolds, tensor fields, differential forms, Lie groups, G-manifolds and symplectic algebra and geometry for theoretical physicists
- Prepares the reader to access the research literature in Hamiltonian mechanics and related areas
- Complete account to Marsden-Weinstein reduction, including the singular case
- Detailed examples for all methods
- Includes supplementary material: sn.pub/extras
Part of the book series: Theoretical and Mathematical Physics (TMP)
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Table of contents (12 chapters)
Keywords
About this book
Starting from an undergraduate level, this book systematically develops the basics of
• Calculus on manifolds, vector bundles, vector fields and differential forms,
• Lie groups and Lie group actions,
• Linear symplectic algebra and symplectic geometry,
• Hamiltonian systems, symmetries and reduction, integrable systems and Hamilton-Jacobi theory.
The topics listed under the first item are relevant for virtually all areas of mathematical physics. The second and third items constitute the link between abstract calculus and the theory of Hamiltonian systems. The last item provides an introduction to various aspects of this theory, including Morse families, the Maslov class and caustics.
The book guides the reader from elementary differential geometry to advanced topics in the theory of Hamiltonian systems with the aim of making current research literature accessible. The style is that of a mathematical textbook,with full proofs given in the text or as exercises. The material is illustrated by numerous detailed examples, some of which are taken up several times for demonstrating how the methods evolve and interact.
Reviews
From the reviews:
“The book is the first of two volumes on differential geometry and mathematical physics. The present volume deals with manifolds, Lie groups, symplectic geometry, Hamiltonian systems and Hamilton-Jacobi theory. … There are several examples and exercises scattered throughout the book. The presentation of material is well organized and clear. The reading of the book gives real satisfaction and pleasure since it reveals deep interrelations between pure mathematics and theoretical physics.” (Tomasz Rybicki, Mathematical Reviews, October, 2013)Authors and Affiliations
Bibliographic Information
Book Title: Differential Geometry and Mathematical Physics
Book Subtitle: Part I. Manifolds, Lie Groups and Hamiltonian Systems
Authors: Gerd Rudolph, Matthias Schmidt
Series Title: Theoretical and Mathematical Physics
DOI: https://doi.org/10.1007/978-94-007-5345-7
Publisher: Springer Dordrecht
eBook Packages: Physics and Astronomy, Physics and Astronomy (R0)
Copyright Information: Springer Science+Business Media Dordrecht 2013
Hardcover ISBN: 978-94-007-5344-0Published: 10 November 2012
Softcover ISBN: 978-94-017-8198-5Published: 14 December 2014
eBook ISBN: 978-94-007-5345-7Published: 09 November 2012
Series ISSN: 1864-5879
Series E-ISSN: 1864-5887
Edition Number: 1
Number of Pages: XIV, 762
Topics: Mathematical Methods in Physics, Global Analysis and Analysis on Manifolds, Classical Mechanics, Topological Groups, Lie Groups, Differential Geometry