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

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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.

FORMATPaperback LANGUAGEEnglish CONDITIONBrand New Publisher Description

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.

Back Cover

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.

Author Biography

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.

Table of Contents

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.

Review

"Assuming an introductory course on differential geometry and some basic knowledge of special relativity, both of which are summarized in the appendices, the book expounds the mathematical background behind the well-established standard model of modern particle and high energy physics… I believe that the book will be a standard textbook on the standard model for mathematics-oriented students." (Hirokazu Nishimura, zbMATH 1390.81005)

Review Quote

"Assuming an introductory course on differential geometry and some basic knowledge of special relativity, both of which are summarized in the appendices, the book expounds the mathematical background behind the well-established standard model of modern particle and high energy physics... I believe that the book will be a standard textbook on the standard model for mathematics-oriented students." (Hirokazu Nishimura, zbMATH 1390.81005)

Feature

Explains the Standard Model to students of both mathematics and physics Covers both the specific gauge theory of the Standard Model and generalizations Highly accessible and self-contained

Description for Sales People

Explains the Standard Model to students of both mathematics and physics Covers both the specific gauge theory of the Standard Model and generalizations Highly accessible and self-contained

Details ISBN3319684388 Author Mark J.D. Hamilton Publisher Springer International Publishing AG Series Universitext Edition 1st ISBN-10 3319684388 ISBN-13 9783319684383 Format Paperback Imprint Springer International Publishing AG Subtitle With Applications to the Standard Model of Particle Physics Place of Publication Cham Country of Publication Switzerland Year 2018 Pages 658 Publication Date 2018-01-10 Media Book DEWEY 530.14/35 Short Title Mathematical Gauge Theory Language English DOI 10.1007/978-3-319-68439-0 UK Release Date 2018-01-10 Illustrations 40 Illustrations, black and white; XVIII, 658 p. 40 illus. Edition Description 1st ed. 2017 Audience Professional & Vocational We've got this

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