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Topology and Geometry for Physics

  • Book
  • © 2011

Overview

Authors:
  1. Helmut Eschrig

    1. IFW Dresden, Dresden, Germany

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  • 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
  • Includes supplementary material: sn.pub/extras

Part of the book series: Lecture Notes in Physics (LNP, volume 822)

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Table of contents (9 chapters)

  1. Front Matter

    Pages i-xii
    Download chapter PDF

  2. Introduction

    • Helmut Eschrig
    Pages 1-9

  3. Topology

    • Helmut Eschrig
    Pages 11-53

  4. Manifolds

    • Helmut Eschrig
    Pages 55-95

  5. Tensor Fields

    • Helmut Eschrig
    Pages 97-114

  6. Integration, Homology and Cohomology

    • Helmut Eschrig
    Pages 115-171

  7. Lie Groups

    • Helmut Eschrig
    Pages 173-204

  8. Bundles and Connections

    • Helmut Eschrig
    Pages 205-246

  9. Parallelism, Holonomy, Homotopy and (Co)homology

    • Helmut Eschrig
    Pages 247-298

  10. Riemannian Geometry

    • Helmut Eschrig
    Pages 299-346

  11. Back Matter

    Pages 347-389
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Keywords

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)

Authors and Affiliations

  • IFW Dresden, Dresden, Germany

    Helmut Eschrig

Bibliographic Information

  • Book Title: Topology and Geometry for Physics

  • Authors: Helmut Eschrig

  • Series Title: Lecture Notes in Physics

  • DOI: https://doi.org/10.1007/978-3-642-14700-5

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Physics and Astronomy, Physics and Astronomy (R0)

  • Copyright Information: Springer-Verlag Berlin Heidelberg 2011

  • Softcover ISBN: 978-3-642-14699-2Published: 09 February 2011

  • eBook ISBN: 978-3-642-14700-5Published: 26 January 2011

  • Series ISSN: 0075-8450

  • Series E-ISSN: 1616-6361

  • Edition Number: 1

  • Number of Pages: XII, 390

  • Number of Illustrations: 60 b/w illustrations

  • Topics: Mathematical Methods in Physics

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