© 2017

Mathematical Gauge Theory

With Applications to the Standard Model of Particle Physics


  • 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


Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages i-xviii
  2. Mathematical Foundations

    1. Front Matter
      Pages 1-1
    2. Mark J. D. Hamilton
      Pages 127-192
    3. Mark J. D. Hamilton
      Pages 193-255
    4. Mark J. D. Hamilton
      Pages 257-318
    5. Mark J. D. Hamilton
      Pages 319-398
  3. The Standard Model of Elementary Particle Physics

    1. Front Matter
      Pages 399-399
    2. Mark J. D. Hamilton
      Pages 401-444
    3. Mark J. D. Hamilton
      Pages 445-526
  4. Appendix

    1. Front Matter
      Pages 601-601
    2. Mark J. D. Hamilton
      Pages 603-623
  5. Back Matter
    Pages 641-657

About this book


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.


gauge theory gauge theory mathematics standard model of elementary particle physics spontaneous symmetry breaking HIggs boson standard model Higss boson electroweak interaction quantum chromodynamics qcd theory grand unified theory Lagrangian principal bundle vector bundle connections and curvature spinor gauge theory of the Standard Model gauge theory and Lagrangians MSC (2010) 55R10, 53C05, 22E70, 15A66, 53C27, 57S15, 22E60 81T13, 81R40, 81V19, 81V05, 81V10, 81V15

Authors and affiliations

  1. 1.Department of MathematicsLudwig-Maximilian University of MunichMunichGermany

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.

Bibliographic information


“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)