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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.
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