Mathematical Gauge Theory: With Applications to the Standard Model of Particle Physics (Universitext)

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. Front Matter ....Pages i-xviii Front Matter ....Pages 1-1 Chapter 1 Lie Groups and Lie Algebras: Basic Concepts (Mark J. D. Hamilton)....Pages 3-82 Chapter 2 Lie Groups and Lie Algebras: Representations and Structure Theory (Mark J. D. Hamilton)....Pages 83-126 Chapter 3 Group Actions (Mark J. D. Hamilton)....Pages 127-192 Chapter 4 Fibre Bundles (Mark J. D. Hamilton)....Pages 193-255 Chapter 5 Connections and Curvature (Mark J. D. Hamilton)....Pages 257-318 Chapter 6 Spinors (Mark J. D. Hamilton)....Pages 319-398 Front Matter ....Pages 399-399 Chapter 7 The Classical Lagrangians of Gauge Theories (Mark J. D. Hamilton)....Pages 401-444 Chapter 8 The Higgs Mechanism and the Standard Model (Mark J. D. Hamilton)....Pages 445-526 Chapter 9 Modern Developments and Topics Beyond the Standard Model (Mark J. D. Hamilton)....Pages 527-599 Front Matter ....Pages 601-601 Appendix A: Background on Differentiable Manifolds (Mark J. D. Hamilton)....Pages 603-623 Appendix B: Background on Special Relativity and Quantum Field Theory (Mark J. D. Hamilton)....Pages 625-640 Back Matter ....Pages 641-657