Differential Geometry and Mathematical Physics: Part I. Manifolds, Lie Groups and Hamiltonian Systems (Theoretical and Mathematical Physics) - Softcover

Rudolph, Gerd; Schmidt, Matthias

Softcover

ISBN 10: 9401781982 ISBN 13: 9789401781985

Publisher: Springer, 2014

Synopsis

This book methodically covers Analysis on manifolds, Lie groups and G-manifolds; Symplectic algebra and geometry, Hamiltonian systems, symmetries and reduction; Integrable systems and Hamilton-Jacobi theory, including Morse families, the Maslov class and more.

About this title

From the Back Cover

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.

Review

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)

Edition details

• Publisher: Springer
• Publication date: 2014
• ISBN 10: 9401781982
• ISBN 13: 9789401781985
• Binding: Paperback
• Language: English
• Number of pages: 776