Unitary Symmetry and Elementary Particles

Unitary Symmetry and Elementary Particles, Second Edition presents the role of symmetry in the study of the physics of the elementary particles. This book discusses the nature and scope of unitary symmetry in physics. Comprised of 12 chapters, this edition starts with an overview of the theories of electromagnetism and gravitation to describe the behavior of certain physical systems. This text then examines the two main categories of the mathematical properties of groups, namely, the properties of abstract groups and the properties of representations of groups. Other chapters consider the use of group theory, which is a significant tool in studying symmetry. This book discusses as well the states that are the basis vectors of irreducible unitary representations of Lie group. The final chapter deals with the quark model, which provides a useful way to understand many properties of hadrons in terms of simpler entities. This book is a valuable resource for physicists.

Preface to Second Edition

Preface to First Edition

1. 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 Symmetry

2. 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 Subgroups

3. 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 Laws

4. 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 S3

5. 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 Algebras

6. 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 Operators

7. 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 Theorem

9. 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 Decays

10. 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 Breaking

11. 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?

References

Index