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E-book
Author Robinson, Matthew B., 1981-

Title Symmetry and the standard model : mathematics and particle physics / Matthew Robinson ; [contributing authors, Jay Dittmann, Karen Bland, Mario Serna, and Gerald Cleaver]
Published New York : Springer, ©2011

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Description 1 online resource (xix, 327 pages) : illustrations
Contents Symmetry and the Standard Model; Preface; Acknowledgments; Contents; Contributing Authors; Chapter 1: Review of Classical Physics; 1.1 Hamilton's Principle; 1.2 Noether's Theorem; 1.3 Conservation of Energy; 1.4 Special Relativity; 1.4.1 Dot Products and Metrics; 1.4.2 The Theory of Special Relativity; 1.4.3 Lorentz Transformations Revisited; 1.4.4 Special Relativity and Lagrangians; 1.4.5 Relativistic Energy-Momentum Relationship; 1.4.6 Physically Allowable Transformations; 1.5 Classical Fields; 1.6 Classical Electrodynamics; 1.7 Classical Electrodynamics Lagrangian
1.8 Gauge Transformations1.9 References and Further Reading; Chapter 2: A Preview of Particle Physics: The Experimentalist's Perspective; 2.1 The Ultimate À̀toms''; 2.2 Quarks and Leptons; 2.3 The Fundamental Interactions; 2.3.1 Gravitation; 2.3.2 Electromagnetism; 2.3.3 The Strong Interaction; 2.3.4 The Weak Interaction; 2.3.5 Summary; 2.4 Categorizing Particles; 2.4.1 Fermions and Bosons; 2.4.2 Baryons and Mesons; 2.4.3 Visualizing the Particle Hierarchy; 2.5 Relativistic Quantum Field Theories of the Standard Model; 2.5.1 Quantum Electrodynamics (QED)
2.5.2 The Unified Electroweak Theory2.5.3 Quantum Chromodynamics (QCD); 2.6 The Higgs Boson; 2.7 References and Further Reading; Chapter 3: Algebraic Foundations; 3.1 Introduction to Group Theory; 3.1.1 What is a Group?; 3.1.2 Definition of a Group; 3.1.3 Finite Discrete Groups and Their Organization; 3.1.4 Group Actions; 3.1.5 Representations; 3.1.6 Reducibility and Irreducibility: A Preview; 3.1.7 Algebraic Definitions; 3.1.8 Reducibility Revisited; 3.2 Introduction to Lie Groups; 3.2.1 Classification of Lie Groups; 3.2.2 Generators; 3.2.3 Lie Algebras; 3.2.4 The Adjoint Representation
3.2.5 SO(2)3.2.6 SO(3); 3.2.7 SU(2); 3.2.8 SU(2) and Physical States; 3.2.9 SU(2) for j=1 2; 3.2.10 SU(2) for j=1; 3.2.11 SU(2) for Arbitrary j; 3.2.12 Root Space; 3.2.13 Adjoint Representation of SU(2); 3.2.14 SU(2) for Arbitrary j ... Again; 3.2.15 SU(3); 3.2.16 What is the Point of All of This?; 3.3 The Lorentz Group; 3.3.1 The Lorentz Algebra; 3.3.2 The Underlying Structure of the Lorentz Group; 3.3.3 Representations of the Lorentz Group; 3.3.3.1 The (0,0) Representation; 3.3.3.2 The (12, 0) Representation; 3.3.3.3 The (0, 12) Representation
3.3.3.4 The Relationship Between (12, 0) and (0, 12)3.3.3.5 The (1/2, 1/2) Representation; 3.3.4 The Vector Representation in Arbitrary Dimension; 3.3.5 Spinor Indices; 3.3.6 Clifford Algebras; 3.4 References and Further Reading; Chapter 4: First Principles of Particle Physics and the Standard Model; 4.1 Quantum Fields; 4.2 Spin-0 Fields; 4.2.1 Equation of Motion for Scalar Fields; 4.2.2 Lagrangian for Scalar Fields; 4.2.3 Solutions to the Klein-Gordon Equation; 4.3 Spin-1/2 Fields; 4.3.1 A Brief Review of Spin; 4.3.2 A Geometric Picture of Spin; 4.3.3 Spin-1/2 Fields
Summary "The first volume of a series intended to teach math in a way that is catered to physicists. Following a brief review of classical physics at the undergraduate level and a preview of particle physics from an experimentalist's perspective, the text systematically lays the mathematical groundwork for an algebraic understanding of the Standard model of particle physics. It then concludes with an overview of the extensions of the previous ideas to physics beyond the standard model. The text is geared toward advanced undergraduate students and first-year graduate students."--Page 4 of cover
This volume "will emphasize algebra, primarily group theory. In the first part we will discuss at length the nature of group theory and the major related ideas, with a special emphasis on Lie groups. The second part will then use these ideas to build a modern formulation of quantum field theory and the tools that are used in particle physics. In keeping with the theme, the formulations and tools will be approached from a heavily algebraic perspective. Finally, the first volume will discuss the structure of the standard model (again, focusing on the algebraic structure) and the attempts to extend and generalize it."--Page viii-ix
Bibliography Includes bibliographical references and index
Notes Print version record
Subject Standard model (Nuclear physics) -- Mathematics
Particles (Nuclear physics) -- Mathematics
Group theory.
Lie groups.
Quantum field theory -- Mathematics
Physique.
Astronomie.
Group theory
Lie groups
Particles (Nuclear physics) -- Mathematics
Quantum field theory -- Mathematics
Standard model (Nuclear physics) -- Mathematics
Form Electronic book
ISBN 9781441982674
1441982671
1283351234
9781283351232
1441982663
9781441982667