Theoretical and Mathematical Physics

Differential Geometry and Mathematical Physics

Part I. Manifolds, Lie Groups and Hamiltonian Systems

Authors: Rudolph, Gerd, Schmidt, Matthias

  • 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
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  • ISBN 978-94-007-5345-7
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Hardcover $99.95
price for USA
  • ISBN 978-94-007-5344-0
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  • ISBN 978-94-017-8198-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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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)

Table of contents (12 chapters)

Buy this book

eBook $69.99
price for USA (gross)
  • ISBN 978-94-007-5345-7
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $99.95
price for USA
  • ISBN 978-94-007-5344-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $99.95
price for USA
  • ISBN 978-94-017-8198-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Differential Geometry and Mathematical Physics
Book Subtitle
Part I. Manifolds, Lie Groups and Hamiltonian Systems
Authors
Series Title
Theoretical and Mathematical Physics
Copyright
2013
Publisher
Springer Netherlands
Copyright Holder
Springer Science+Business Media Dordrecht
eBook ISBN
978-94-007-5345-7
DOI
10.1007/978-94-007-5345-7
Hardcover ISBN
978-94-007-5344-0
Softcover ISBN
978-94-017-8198-5
Series ISSN
1864-5879
Edition Number
1
Number of Pages
XIV, 762
Topics