Unitary Symmetry and Elementary Particles

Preface to Second EditionPreface to First Edition1. Introduction 1.1 Uses of Symmetry 1.2 Symmetries and Conservation Laws 1.3 Symmetries and Groups 1.4 Eigenstates, Quantum Numbers, and Selection Rules 1.5 A Listing of Symmetries 1.6 Space-Time and Internal Symmetries 1.7 Limitations of Symmetry2. Some Properties of Groups 2.1 Elementary Notions 2.2 Homomorphism, Isomorphism, and Subgroups 2.3 Infinite Groups 2.4 Cosets, Conjugate Classes, and Invariant Subgroups3. Symmetry, Group Representations, and Particle Multiplets 3.1 Linear and Unitary Vector Spaces 3.2 Operators 3.3 Some Properties of Representations 3.4 Unitary Representations, Multiplets, and Conservation Laws4. The Symmetric Group and Identical Particles 4.1 Two- and Three-Particle States 4.2 Standard Arrangements of Young Tableaux 4.3 Basts Functions of S35. Lie Groups and Lie Algebras 5.1 Some Definitions and Examples 5.2 Generators of Lie Groups 5.3 Simple and Semisimple Lie Algebras 5.4 Standard Form of Lie Algebras6. Multiplets 6.1 Diagonal Generators and Weights 6.2 Generators of SU(2) and U(2) 6.3 Generators of SU(3) and U(3) 6.4 Generators of SU(4) and Beyond 6.5 Properties of the Weights 6.6 Weight Diagrams of SU(3) 6.7 Weights of SU(n) 6.8 Casimir Operators and the Labeling of States 6.9 Tensor Operators7. Young Tableaux and Unitary Symmetry 7.1 Dimensionality of Multiplets of SU(n) 7.2 Dimensionality Formulas 7.3 Multiplets of the SU(n-l) Subgroups of SU(n) 7.4 Decomposition of Products of Irreducible Representations 7.5 Classes of Representations 7.6 Multiplets of U(n)8. Clebsch-Gordan Coefficients 8.1 Some Properties of the Coefficients 8.2 Raising and Lowering Operators 8.3 Matrix Representation of the Algebra of SU(n) 8.4 Clebsch-Gordan Coefficients of SU(2) 8.5 Clebsch-Gordan Coefficients of SU(3) 8.6 Clebsch-Gordan Coefficients of SU(4) and Beyond 8.7 Other Matrix Representations of the Algebra of SU(n) 8.8 Wigner-Eckart Theorem9. The Eightfold Way 9.1 SU(3) and Hadrons 9.2 Baryon Multiplets 9.3 Meson Multiplets 9.4 U-Spin 9.5 Tests of U-Spin Invariance 9.6 Gell-Mann-Okubo Mass Formula 9.7 Meson-Baryon Coupling 9.8 Hadron Decays 9.9 Weak Hadron Decays10. Charm 10.1 Need for a New Quantum Number 10.2 Heavy Mesons with and without Charm 10.3 Charmed Baryons 10.4 SU(4) Symmetry Breaking11. Approximate SU(6) and SU(8) 11.1 Dynamical Symmetry 11.2 Classification of Hadrons in SU(6) 11.3 Classification of Hadrons in SU(8) 11.4 Troubles with SU(6) and SU(8)12. The Quark Model 12.1 Predecessors to the Quark Model 12.2 Quarks with Flavor, Including Charm 12.3 Colored Quarks 12.4 Quarks and Local Gauge Field Theory 12.5 Baryon and Meson Wave Functions 12.6 SU(6), SU(8), and the Quark Model 12.7 Baryon Magnetic Moments 12.8 Hadron Mass Splittings 12.9 Hadron Decays and Zweig's Rule 12.10 Diquarks and Exotic Hadrons 12.11 Orbital Excitations 12.12 High Energy Scattering 12.13 A Fifth Quark? 12.14 Where Are the Quarks? ReferencesIndex