Differential Geometry and Mathematical Physics

Part I. Manifolds, Lie Groups and Hamiltonian Systems

  • Gerd Rudolph
  • Matthias Schmidt

Part of the Theoretical and Mathematical Physics book series (TMP)

Table of contents

  1. Front Matter
    Pages I-XIII
  2. Gerd Rudolph, Matthias Schmidt
    Pages 1-51
  3. Gerd Rudolph, Matthias Schmidt
    Pages 53-92
  4. Gerd Rudolph, Matthias Schmidt
    Pages 93-164
  5. Gerd Rudolph, Matthias Schmidt
    Pages 165-217
  6. Gerd Rudolph, Matthias Schmidt
    Pages 219-267
  7. Gerd Rudolph, Matthias Schmidt
    Pages 269-314
  8. Gerd Rudolph, Matthias Schmidt
    Pages 315-352
  9. Gerd Rudolph, Matthias Schmidt
    Pages 353-425
  10. Gerd Rudolph, Matthias Schmidt
    Pages 427-490
  11. Gerd Rudolph, Matthias Schmidt
    Pages 491-567
  12. Gerd Rudolph, Matthias Schmidt
    Pages 569-640
  13. Gerd Rudolph, Matthias Schmidt
    Pages 641-727
  14. Back Matter
    Pages 729-759

About this book

Introduction

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.

Keywords

Analysis on Manifolds Differential Geometry Applied Hamilton-Jacobi Theory Hamiltonian Systems Integrable Systems Lie Groups Applied Manifold Symmetries and Reduction Symplectic Geometry Symplectic Reduction

Authors and affiliations

  • Gerd Rudolph
    • 1
  • Matthias Schmidt
    • 2
  1. 1.Institute for Theoretical PhysicsUniversity of LeipzigLeipzigGermany
  2. 2.Institute for Theoretical PhysicsUniversity of LeipzigLeipzigGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-94-007-5345-7
  • Copyright Information Springer Science+Business Media Dordrecht 2013
  • Publisher Name Springer, Dordrecht
  • eBook Packages Physics and Astronomy
  • Print ISBN 978-94-007-5344-0
  • Online ISBN 978-94-007-5345-7
  • Series Print ISSN 1864-5879
  • Series Online ISSN 1864-5887
  • About this book