Mathematical Gauge Theory: With Applications to the Standard Model of Particle Physics (Universitext)
Explains the Standard Model to students of both mathematics andphysicsCovers both the specific gauge theory of the Standard Model andgeneralizationsHighly accessible and self-contained——————————The Standard Model is the foundation of modern particle and highenergy physics. This book explains the mathematical backgroundbehind the Standard Model, translating ideas from physics into amathematical language and vice versa.The first part of the book covers the mathematical theory of Liegroups and Lie algebras, fibre bundles, connections, curvature andspinors. The second part then gives a detailed exposition of howthese concepts are applied in physics, concerning topics such asthe Lagrangians of gauge and matter fields, spontaneous symmetrybreaking, the Higgs boson and mass generation of gauge bosons andfermions. The book also contains a chapter on advanced and moderntopics in particle physics, such as neutrino masses, CP violationand Grand Unification.This carefully written textbook is aimed at graduate students ofmathematics and physics. It contains numerous examples and morethan 150 exercises, making it suitable for self-study and usealongside lecture courses. Only a basic knowledge of differentiablemanifolds and special relativity is required, summarized in theappendix.