Lecture Notes in Physics

Topology and Geometry for Physics

Authors: Eschrig, Helmut

  • Covers all the important topics of topology and geometry in physics in a very comprehensive way
  • Completely closed presentation of topological concepts for theoretical physics
  • Didactically well written
  • Mathematically strict level
  • A valuable textbook for students of theoretical physics
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eBook $59.99
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  • ISBN 978-3-642-14700-5
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  • Immediate eBook download after purchase
Softcover $79.95
price for USA
  • ISBN 978-3-642-14699-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
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About this book

A concise but self-contained introduction of the central concepts of modern topology and differential geometry on a mathematical level is given specifically with applications in physics in mind. All basic concepts are systematically provided including sketches of the proofs of most statements. Smooth finite-dimensional manifolds, tensor and exterior calculus operating on them, homotopy, (co)homology theory including Morse theory of critical points, as well as the theory of fiber bundles and Riemannian geometry, are treated. Examples from physics comprise topological charges, the topology of periodic boundary conditions for solids, gauge fields, geometric phases in quantum physics and gravitation.

Reviews

From the reviews:

“It consists of nine main chapters … and the final Compendium which summarizes the volume in thirty two pages the basic geometric concepts and facts used in the book. … the author really has achieved his purpose, namely he wrote a book rigorous in a mathematical sense, nevertheless not over-loaded by the physically non-necessary proofs and mathematical details, and at the same time giving to the reader a rigorous mathematical explanation of physical phenomena, often quite recently discovered and not commonly known.” (Jan Jerzy Sławianowski, Journal of Geometry and Symmetry in Physics, Vol. 25, 2012)

“The author describes well the purpose of this text. It is to present to the theoretical physicist much of modern mathematics s/he may need … with an emphasis on the motivation for the new concepts introduced. … The resulting book achieves these aims to a large extent. The new concepts are motivated … from physical examples before a precise definition is given. … Altogether this book contains a lot of useful material … written in a very concise style.” (Hans-Peter Künzle, Mathematical Reviews, Issue 2012 a)

“The book is intended as bridging material between advanced graduate textbooks of modern analysis and mathematical physics … . The text is of high quality and has the explicit aim to summarize and communicate current knowledge in an accessible way. The book mainly addresses students in solid state and statistical physics regarding the focus and the choice of examples of application, but it can be useful for particle physicists, too.” (S. Moskaliuk, Zentralblatt MATH, Vol. 1222, 2011)


Table of contents (9 chapters)

Buy this book

eBook $59.99
price for USA (gross)
  • ISBN 978-3-642-14700-5
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $79.95
price for USA
  • ISBN 978-3-642-14699-2
  • 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
Topology and Geometry for Physics
Authors
Series Title
Lecture Notes in Physics
Series Volume
822
Copyright
2011
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-14700-5
DOI
10.1007/978-3-642-14700-5
Softcover ISBN
978-3-642-14699-2
Series ISSN
0075-8450
Edition Number
1
Number of Pages
XII, 390
Number of Illustrations and Tables
60 b/w illustrations
Topics