Description
Taylor & Francis Ltd Group Theory For The Standard Model Of Particle Physics And Beyond 2010 Edition by Ken J. Barnes
Based on the author's well-established courses, Group Theory for the Standard Model of Particle Physics and Beyond explores the use of symmetries through descriptions of the techniques of Lie groups and Lie algebras. The text develops the models, theoretical framework, and mathematical tools to understand these symmetries.After linking symmetries with conservation laws, the book works through the mathematics of angular momentum and extends operators and functions of classical mechanics to quantum mechanics. It then covers the mathematical framework for special relativity and the internal symmetries of the standard model of elementary particle physics. In the chapter on Noether's theorem, the author explains how Lagrangian formalism provides a natural framework for the quantum mechanical interpretation of symmetry principles. He then examines electromagnetic, weak, and strong interactions; spontaneous symmetry breaking; the elusive Higgs boson; and supersymmetry. He also introduces new techniques based on extending space-time into dimensions described by anticommuting coordinates.Designed for graduate and advanced undergraduate students in physics, this text provides succinct yet complete coverage of the group theory of the symmetries of the standard model of elementary particle physics. It will help students understand current knowledge about the standard model as well as the physics that potentially lies beyond the standard model. Symmetries and Conservation LawsLagrangian and Hamiltonian Mechanics Quantum MechanicsCoupled Oscillators: Normal Modes One-Dimensional Fields: Waves The Final Step: Lagrange-Hamilton Quantum Field TheoryQuantum Angular MomentumIndex Notation Quantum Angular Momentum Result Matrix Representations Spin 1/2Addition of Angular Momenta Clebsch-Gordan CoefficientsMatrix Representation of Direct (Outer, Kronecker) Products Change of BasisTensors and Tensor OperatorsScalars Scalar FieldsInvariant Functions Contravariant Vectors (t index at top) Covariant Vectors (Co = Goes Below) NotesTensorsRotations Vector Fields Tensor OperatorsConnection with Quantum MechanicsSpecification of Rotations Transformation of Scalar Wave FunctionsFinite Angle Rotations Consistency with the Angular Momentum Commutation RulesRotation of Spinor Wave Function Orbital Angular Momentum (x x p) The Spinors RevisitedDimensions of Projected SpacesConnection between the "Mixed Spinor" and the Adjoint (Regular) Representation Finite Angle Rotation of SO(3) VectorSpecial Relativity and the Physical Particle StatesThe Dirac Equation The Clifford Algebra: Properties of Matrices Structure of the Clifford Algebra and Representation Lorentz Covariance of the Dirac Equation The Adjoint The Nonrelativistic Limit Poincare Group: Inhomogeneous Lorentz Group Homogeneous (Later Restricted) Lorentz GroupPoincare AlgebraThe Casimir Operators and the StatesInternal SymmetriesLie Group Techniques for the Standard Model Lie GroupsRoots and Weights Simple Roots The Cartan Matrix Finding All the Roots Fundamental Weights The Weyl Group Young Tableaux Raising the Indices The Classification Theorem (Dynkin) Result Coincidences Noether's Theorem and Gauge Theories of the First and Second KindsBasic Couplings of the Electromagnetic, Weak, and Strong InteractionsSpontaneous Symmetry Breaking and the Unification of the Electromagnetic and Weak ForcesThe Goldstone Theorem and the Consequent Emergence on Nonlinear Transforming Massless Goldstone BosonsThe Higgs Mechanism and the Emergence of Mass from Spontaneously Broken SymmetriesLie Group Techniques for beyond the Standard Model Lie GroupsThe Simple SphereBeyond the Standard ModelMassive CaseMassless Case Projection OperatorsWeyl Spinors and Representation Charge Conjugation and Majorana Spinor A Notational TrickSL(2, C) View Unitary Representations Supersymmetry: A First Look at the Simplest (N = 1) Case Massive Representations Massless Representations Superspace Three Dimensional Euclidean Space (Revisited) Covariant Derivative Operators from Right Action Superfields SupertransformationsThe Chiral Scalar Multiplet Superspace Methods Covariant Definition of Component Fields Supercharges Revisited Invariants and LagrangiansSuperpotentialReferences and Problems appear at the end of each chapter.