Mathematical Gauge Theory

With Applications to the Standard Model of Particle Physics
1. Auflage 2017
ISBN: 978-3-319-68438-3
Verlag: Springer Nature Switzerland

Buch, Englisch, 658 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 10059 g

Reihe: 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.

Zielgruppe

Graduate

Autoren/Hrsg.

Hamilton, Mark J. D.

Fachgebiete

• Mathematik | Informatik Mathematik Geometrie Analytische Geometrie
• Naturwissenschaften Physik Quantenphysik Teilchenphysik
• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
• Mathematik | Informatik Mathematik Topologie Analytische Topologie
• Mathematik | Informatik Mathematik Geometrie Differentialgeometrie
• Mathematik | Informatik Mathematik Topologie Algebraische Topologie

Inhaltsverzeichnis

Part I Mathematical foundations.- 1 Lie groups and Lie algebras: Basic concepts.- 2 Lie groups and Lie algebras: Representations and structure theory.- 3 Group actions.- 4 Fibre bundles.- 5 Connections and curvature.- 6 Spinors.- Part II The Standard Model of elementary particle physics.- 7 The classical Lagrangians of gauge theories.- 8 The Higgs mechanism and the Standard Model.- 9 Modern developments and topics beyond the Standard Model.- Part III Appendix.- A Background on differentiable manifolds.- B Background on special relativity and quantum field theory.- References.- Index.

Über Autor(innen)

Mark Hamilton has worked as a lecturer and interim professor at the University of Stuttgart and the Ludwig-Maximilian University of Munich. His research focus lies on geometric topology and mathematical physics, in particular, the differential topology of 4-manifolds and Seiberg-Witten theory.