Group theory for the standard model of particle physics and beyond. (©2010)

• Record Type: Book
• Further Information: Note: Ken J. Barnes.
• Other Names: Barnes, Ken J, 1938-
• Contents: Symmetries and Conservation Laws Lagrangian and Hamiltonian Mechanics Quantum Mechanics Coupled Oscillators: Normal Modes One-Dimensional Fields: Waves The Final Step: Lagrange–Hamilton Quantum Field Theory Quantum Angular Momentum Index Notation Quantum Angular Momentum Result Matrix Representations Spin 1/2 Addition of Angular Momenta Clebsch–Gordan Coefficients Matrix Representation of Direct (Outer, Kronecker) Products Change of Basis Tensors and Tensor Operators Scalars Scalar Fields Invariant Functions Contravariant Vectors (t →index at top) Covariant Vectors (Co = Goes Below) Notes Tensors Rotations Vector Fields Tensor Operators Connection with Quantum Mechanics Specification of Rotations Transformation of Scalar Wave Functions Finite Angle Rotations Consistency with the Angular Momentum Commutation Rules Rotation of Spinor Wave Function Orbital Angular Momentum (x × p ) The Spinors Revisited Dimensions of Projected Spaces Connection between the "Mixed Spinor" and the Adjoint (Regular) Representation Finite Angle Rotation of SO (3) Vector Special Relativity and the Physical Particle States The Dirac Equation The Clifford Algebra: Properties of γ Matrices Structure of the Clifford Algebra and Representation Lorentz Covariance of the Dirac Equation The Adjoint The Nonrelativistic Limit Poincaré Group: Inhomogeneous Lorentz Group Homogeneous (Later Restricted) Lorentz Group Poincaré Algebra The Casimir Operators and the States Internal Symmetries Lie Group Techniques for the Standard Model Lie Groups Roots 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 Kinds Basic Couplings of the Electromagnetic, Weak, and Strong Interactions Spontaneous Symmetry Breaking and the Unification of the Electromagnetic and Weak Forces The Goldstone Theorem and the Consequent Emergence on Nonlinear Transforming Massless Goldstone Bosons The Higgs Mechanism and the Emergence of Mass from Spontaneously Broken Symmetries Lie Group Techniques for beyond the Standard Model Lie Groups The Simple Sphere Beyond the Standard Model Massive Case Massless Case Projection Operators Weyl Spinors and Representation Charge Conjugation and Majorana Spinor A Notational Trick SL (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 Supertransformations The Chiral Scalar Multiplet Superspace Methods Covariant Definition of Component Fields Supercharges Revisited Invariants and Lagrangians Superpotential References and Problems appear at the end of each chapter.
• Publisher Details: Boca Raton [Fla.] : CRC Press/Taylor & Francis
• Publication Date: 2010
• Copyright Date: 2010
• Extent: 1 online resource (xiii, 241 pages)
• Subjects: 539.725; Group theory; Quantum theory; Particle range (Nuclear physics); Group theory; Particle range (Nuclear physics); Quantum theory; Electronic books
• Languages: English
• ISBNs: 9781439895207; 1439895201
• Notes: Note: Includes bibliographical references and index.
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.