Hamilton M.J.D. Mathematical Gauge Theory: With Applications to the Standard Model of Particle Physics

Springer International Publishing AG, 2017. — 667 p. — (Universitext) — ISBN: 978-3-319-68439-0.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.Mathematical Foundations
Lie Groups and Lie Algebras: Basic Concepts
Lie Groups and Lie Algebras: Representations and Structure Theory
GroupActions
Fibre Bundles
Connections and Curvature
Spinors
The Standard Model of Elementary Particle Physics
The Classical Lagrangians of Gauge Theories
The Higgs Mechanism and the Standard Model
Modern Developments and Topics Beyond the Standard Model
Appendixes
Background on DifferentiableManifolds
Background on Special Relativity and Quantum Field Theory