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Universitext

Mathematical Gauge Theory

With Applications to the Standard Model of Particle Physics

Authors: Hamilton, Mark

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  • Explains the Standard Model to students of both mathematics and physics
  • Covers both the specific gauge theory of the Standard Model and generalizations
  • Highly accessible and self-contained
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eBook $79.99
price for USA in USD (gross)
  • ISBN 978-3-319-68439-0
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $99.99
price for USA in USD
  • ISBN 978-3-319-68438-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this Textbook

The Standard Model is the foundation of modern particle and high energy physics. This book explains the mathematical background behind the Standard Model, translating ideas from physics into a mathematical language and vice versa.

The first part of the book covers the mathematical theory of Lie groups and Lie algebras, fibre bundles, connections, curvature and spinors. The second part then gives a detailed exposition of how these concepts are applied in physics, concerning topics such as the Lagrangians of gauge and matter fields, spontaneous symmetry breaking, the Higgs boson and mass generation of gauge bosons and fermions. The book also contains a chapter on advanced and modern topics in particle physics, such as neutrino masses, CP violation and Grand Unification.

This carefully written textbook is aimed at graduate students of mathematics and physics. It contains numerous examples and more than 150 exercises, making it suitable for self-study and use alongside lecture courses. Only a basic knowledge of differentiable manifolds and special relativity is required, summarized in the appendix.

About the authors

Mark Hamilton has worked as a lecturer and interim professor at the University of Stuttgart and the Ludwig-Maximilian University of Munich. His research focus lies on geometric topology and mathematical physics, in particular, the differential topology of 4-manifolds and Seiberg-Witten theory.

Reviews

“Assuming an introductory course on differential geometry and some basic knowledge of special relativity, both of which are summarized in the appendices, the book expounds the mathematical background behind the well-established standard model of modern particle and high energy physics… I believe that the book will be a standard textbook on the standard model for mathematics-oriented students.” (Hirokazu Nishimura, zbMATH 1390.81005)

Table of contents (11 chapters)

Table of contents (11 chapters)
  • Chapter 1 Lie Groups and Lie Algebras: Basic Concepts

    Pages 3-82

    Hamilton, Mark J. D.

  • Chapter 2 Lie Groups and Lie Algebras: Representations and Structure Theory

    Pages 83-126

    Hamilton, Mark J. D.

  • Chapter 3 Group Actions

    Pages 127-192

    Hamilton, Mark J. D.

  • Chapter 4 Fibre Bundles

    Pages 193-255

    Hamilton, Mark J. D.

  • Chapter 5 Connections and Curvature

    Pages 257-318

    Hamilton, Mark J. D.

Buy this book

eBook $79.99
price for USA in USD (gross)
  • ISBN 978-3-319-68439-0
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $99.99
price for USA in USD
  • ISBN 978-3-319-68438-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Mathematical Gauge Theory
Book Subtitle
With Applications to the Standard Model of Particle Physics
Authors
Series Title
Universitext
Copyright
2017
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing AG
eBook ISBN
978-3-319-68439-0
DOI
10.1007/978-3-319-68439-0
Softcover ISBN
978-3-319-68438-3
Series ISSN
0172-5939
Edition Number
1
Number of Pages
XVIII, 658
Number of Illustrations
40 b/w illustrations
Topics