Unitary Symmetry and Elementary Particles (eBook)

D. B. Lichtenberg (Autor)

eBook Download: PDF

2013 | 1. Auflage
262 Seiten
Elsevier Science (Verlag)
978-1-4832-6626-8 (ISBN)

Infos

Unitary Symmetry and Elementary Particles discusses the role of symmetry in elementary particle physics. The book reviews the theory of abstract groups and group representations including Eigenstates, cosets, conjugate classes, unitary vector spaces, unitary representations, multiplets, and conservation laws. The text also explains the concept of Young Diagrams or Young Tableaux to prove the basis functions of the unitary irreducible representations of the unitary group SU(n). The book defines Lie groups, Lie algebras, and gives some examples of these groups. The basis vectors of irreducible unitary representations of Lie groups constitute a multiplet, which according to Racah (1965) and Behrends et al. (1962) can have properties of weights. The text also explains the properties of Clebsch-Gordan coefficients and the Wigner-Eckart theorem. SU(3) multiplets have members classified as hadrons (strongly interacting particles), of which one characteristic show that the mass differences of these members have some regular properties. The Gell-Mann and Ne-eman postulate also explains another characteristic peculiar to known multiplets. The book describes the quark model, as well as, the uses of the variants of the quark model. This collection is suitable for researchers and scientists in the field of applied mathematics, nuclear physics, and quantum mechanics.

Inhalt

Front Cover 1
Unitary Symmetry and Elementary Particles 4
Copyright Page 5
Table of Contents 6
PREFACE 10
Acknowledgments 14
CHAPTER 1. INTRODUCTION 18
1.1 Uses of Symmetry 18
1.2 Symmetries and Conservation Laws 19
1.3 Symmetries and Groups 21
1.4 Eigenstates, Quantum Numbers, and Selection Rules 22
1.5 A Listing of Symmetries 23
CHAPTER 2. SOME PROPERTIES OF GROUPS 27
2.1 Elementary Notions 27
2.2 Homomorphism, Isomorphism, and Subgroups 30
2.3 Infinite Groups 31
2.4 Cosets, Conjugate Classes, and Invariant Subgroups 35
CHAPTER 3. SYMMETRY, GROUP REPRESENTATIONS, AND PARTICLE MULTIPLETS 39
3.1 Linear and Unitary Vector Spaces 39
3.2 Operators 42
3.3 Some Properties of Representations 47
3.4 Unitary Representations, Multiplets, and Conservation Laws 50
CHAPTER 4. THE SYMMETRIC GROUP AND IDENTICAL PARTICLES 53
4.1 Two- and Three-Particle States 53
4.2 Standard Arrangements of Young Tableaux 57
4.3 Basis Functions of S3 62
CHAPTER 5. LIE GROUPS AND LIE ALGEBRAS 65
5.1 Some Definitions and Examples 65
5.2 Generators of Lie Groups 67
5.3 Simple and Semisimple Lie Algebras 75
5.4 Standard Form of Lie Algebras 75
CHAPTER 6. MULTIPLETS 83
6.1 Diagonal Generators and Weights 83
6.2 Generators of SU(2) and SU(3) 85
6.3 Properties of the Weights 93
6.4 Weight Diagrams of SU(3) 98
6.5 Casimir Operators and the Labeling of States 104
6.6 Tensor Operators 106
CHAPTER 7. YOUNG TABLEAUX AND UNITARY SYMMETRY 109
7.1 Dimensionality of Multiplets of SU(n) 109
7.2 Dimensionality Formulas 117
7.4 Decomposition of Products of Irreducible Representations 125
7.5 Classes of Representations 130
7.6 Multiplets of U(n) 132
CHAPTER 8. CLEBSCH–GORDAN COEFFICIENTS 133
8.1 Some Properties of the Coefficients 133
8.2 Raising and Lowering Operators 137
8.3 Matrix Representation of the Algebra of SU(n) 140
8.4 Clebsch-Gordan Coefficients of SU(2) 144
8.5 Clebseh–Gordan Coefficients of SU/(3) 150
8.6 Wigner–Eckart Theorem 167
CHAPTER 9. THE EIGHTFOLD WAY 169
9.1 SU{3) and Hadrons 169
9.2 Baryon Multiplets 171
9.3 Meson Multiplets 177
9.4 U-Spin 182
9.5 Tests of U-Spin Invariance 185
9.6 Gell-Mann–Okubo Mass Formula 190
9.7 Meson–Baryon Coupling 195
9.8 Hadron Decays 197
9.9 Weak Hadron Decays 198
CHAPTER 10. APPROXIMATE SU(6) 201
10.1 Dynamical Symmetry 201
10.2 Classification of Hadrons 202
10.3 Matrix Generators of SU(6) 207
10.4 Troubles with SU(6) 209
CHAPTER 11. THE QUARK MODEL 212
11.1 Sakata Triplets 212
11.2 Properties of Quarks 214
11.3 Baryon and Meson Wave Functions 217
11.4 Baryon Magnetic Moments 223
11.5 Hadron Mass Splittings 229
11.6 Quark Model and SU{6) 235
11.7 Orbital Excitations 238
11.8 High Energy Scattering 240
11.9 Troubles with the Quark Model 241
CHAPTER 12. VARIANTS OF THE QUARK MODEL 244
12.1 Examples of Models 244
12.2 Two-Particle Model of Baryons 249
12.3 Dyon Model 251
12.4 Usefulness of the Various Models 252
REFERENCES 254
SUBJECT INDEX 258

Produkt-Details

• Erscheint lt. Verlag: 22.10.2013
• Sprache: englisch
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Quantenphysik
• Themenwelt: Technik
• ISBN-10: 1-4832-6626-5 / 1483266265
• ISBN-13: 978-1-4832-6626-8 / 9781483266268