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

Book Details

• Publisher: Springer

• Author: Mark J. D. Hamilton

• Language: English

• Edition: 2017 Edition

• ISBN: 9783319684383

• Pages: 657

• Cover: Paperback

• Release Date: 10-01-2018

• Dimensions: 9.3 x 6.1 x 1.5 inches

About The Book
The Mathematical Structure of the Standard Model by Mark J. D. Hamilton is an insightful and comprehensive textbook that explains the mathematical foundation behind the Standard Model of particle physics. This book bridges the gap between the abstract concepts of physics and the mathematical language used to describe them, providing a clear and rigorous explanation of the theories that underpin modern particle and high-energy physics.

The book is divided into two parts:

• Mathematical Theory: The first part covers essential mathematical concepts, including Lie groups and Lie algebras, fibre bundles, connections, curvature, and spinors — all fundamental to the mathematical understanding of the Standard Model.

• Applications to Physics: The second part demonstrates how these mathematical concepts are applied in physics. Topics include the Lagrangians of gauge and matter fields, spontaneous symmetry breaking, the Higgs boson, and the mass generation of gauge bosons and fermions.

In addition to these core topics, the book explores more advanced and modern areas of particle physics, such as neutrino masses, CP violation, and Grand Unification. This makes it an excellent resource for graduate students in mathematics and physics.

The book includes more than 150 exercises and numerous examples, making it suitable for self-study and an ideal companion to lecture courses. It assumes a basic understanding of differentiable manifolds and special relativity, which are summarized in the appendix, ensuring that the book is accessible to those with fundamental knowledge in these areas.

The Mathematical Structure of the Standard Model is not just a textbook; it is a thorough and carefully written guide to understanding the mathematical underpinnings of particle physics, destined to become a standard reference for students and researchers in the field.

Mark J. D. Hamilton, a lecturer and researcher with a focus on geometric topology and mathematical physics, brings his expertise to this work, offering a precise and engaging explanation of the mathematical tools used in high-energy physics.