Texts in Applied Mathematics

Topology, Geometry and Gauge fields

Foundations

Authors: Naber, Gregory L.

  • Detailed calculations of a number of concrete examples
  • Written for mathematicians who want to see something of the applications of topology and geometry to modern physics
  • Also aimed at physicists who want to see the foundations of their subject treated with mathematical rigor
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  • ISBN 978-1-4419-7254-5
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  • ISBN 978-1-4614-2682-0
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About this Textbook

This is a book on topology and geometry, and like any book on subjects as vast as these, it has a point of view that guided the selection of topics. The author’s point of view is that the rekindled interest that mathematics and physics have shown in each other of late should be fostered, and that this is best accomplished by allowing them to cohabit. The goal is to weave together rudimentary notions from the classical gauge theories of physics and the topological and geometrical concepts that became the mathematical models of these notions. The reader is assumed to have a minimal understanding of what an electromagnetic field is, a willingness to accept a few of the more elementary pronouncements of quantum mechanics, and a solid background in real analysis and linear algebra with some of the vocabulary of modern algebra. To such a reader we offer an excursion that begins with the definition of a topological space and finds its way eventually to the moduli space of anti-self-dual SU(2)-connections on S4 with instanton number -1. This second edition of the book includes a new chapter on singular homology theory and a new appendix outlining Donaldson’s beautiful application of gauge theory to the topology of compact, simply connected , smooth 4-manifolds with definite intersection form. Reviews of the first edition: “It is unusual to find a book so carefully tailored to the needs of this interdisciplinary area of mathematical physics…Naber combines a deep knowledge of his subject with an excellent informal writing style.” (NZMS Newsletter) "...this book should be very interesting for mathematicians and physicists (as well as other scientists) who are concerned with gauge theories." (ZENTRALBLATT FUER MATHEMATIK) “The book is well written and the examples do a great service to the reader. It will be a helpful companion to anyone teaching or studying gauge theory …” (Mathematical Reviews)

About the authors

Gregory Naber is a Professor at Drexel University in the Department of Mathematics

Reviews

First Edition Review:

"Naber’s book, together with its predecessor[N4] subtitled Foundations, occupies a less populated niche in the market. This is the sector of teachable texts on differential geometry and its use in physics. Teachability does not refer to a definition-theorem-proof format. Nor does it imply anything about the depth of the treatment. Rather, it has to do with the organization of the topics, the selection of examples, the amount of instructive details provided, the ability to anticipate questions from the reader, and knowing when to stop."

--SIAM REVIEW


Table of contents (9 chapters)

Buy this book

eBook $59.99
price for USA (gross)
  • ISBN 978-1-4419-7254-5
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $79.99
price for USA
  • ISBN 978-1-4419-7253-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $79.99
price for USA
  • ISBN 978-1-4614-2682-0
  • 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, Geometry and Gauge fields
Book Subtitle
Foundations
Authors
Series Title
Texts in Applied Mathematics
Series Volume
25
Copyright
2011
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media, LLC
eBook ISBN
978-1-4419-7254-5
DOI
10.1007/978-1-4419-7254-5
Hardcover ISBN
978-1-4419-7253-8
Softcover ISBN
978-1-4614-2682-0
Series ISSN
0939-2475
Edition Number
2
Number of Pages
XX, 437
Topics