ISBN: 3-540-65235-3
TITLE: Fields, Symmetries, and Quarks
AUTHOR: Mosel, Ulrich
TOC:

Part I. Preliminaries
1. Units and Metric 3
1.1 Units 3
1.2 Metric and Notation 4
Part II. Fundamentals of Field Theory
2. Classical Fields 9
2.1 Equations of Motion 9
2.1.1 Examples 11
2.2 Symmetries and Conservation Laws 14
2.2.1 Geometrical SpaceTime Symmetries 15
2.2.2 Internal Symmetries 17
3. Free Fields and Their Quantization 21
3.1 Classification of Fields 21
3.2 Scalar Fields 23
3.2.1 Quantization of the Hermitian Scalar Field 24
3.2.2 Quantization of the Charged Scalar Field 27
3.3 Vector Fields 29
3.3.1 Massive Vector Fields 29
3.3.2 Massless Vector Fields 30
3.4 Fermion Fields 32
3.4.1 Dirac Equation 32
3.4.2 Lagrangian for Fermion Fields 34
3.4.3 Quantization of the Dirac Field 35
3.4.4 Massless Fermions 38
3.4.5 Neutrinos 40
3.5 Transition Rates in Quantum Field Theory 44
3.6 Quantum Mechanical Consistency 52
Part III. Global Symmetries
4. Symmetries of Meson and Baryon Systems 57
4.1 U(1) Symmetry 57
4.1.1 Properties of the Group U(1) 58
4.1.2 Structure of the Nucleon Lagrangian 59
4.2 SU(2) Symmetry 60
4.2.1 Properties of the Group SU(2) 60
4.2.2 General Definitions 64
4.2.3 Application to the PionNucleon System 64
4.2.4 Structure of SU(2) Multiplets 72
4.3 SU(3) Symmetry 74
4.3.1 Properties of the Group SU(3) 75
4.3.2 Structure of SU(3) Multiplets 78
4.3.3 Assignments of Hadrons to SU(3) Multiplets 83
4.3.4 SU(3) Symmetry Breaking 85
5. Quarks 87
5.1 Construction of SU(3) Multiplets 87
5.1.1 Construction of the Representation 3o3 89
5.1.2 Construction of the Representation 3o3o3 90
5.2 State Vectors for the Multiplets 92
5.2.1 Tensor Algebra 93
5.2.2 Hadron Multiplets 96
5.3 Color Degree of Freedom 100
6. Chiral Symmetry 103
6.1 Phenomenology of beta-Decay 103
6.1.1 Leptonic beta-Decay 103
6.1.2 Semileptonic -Decay 104
6.2 Current Conservation in Strong Interactions 106
6.2.1 Vector Current Conservation 106
6.2.2 Axial Vector Current Conservation 108
6.3 Chiral Symmetry Group 110
6.3.1 Chiral Symmetry Transformations for the Fermions 110
6.3.2 Chiral Symmetry Transformations for the Mesons 112
7. Spontaneous Global Symmetry Breaking 115
7.1 Goldstone Theorem 115
7.1.1 Goldstone Bosons 116
7.2 Examples of the Goldstone Mechanism 119
7.2.1 Spontaneous Breaking of a Global Non-Abelian Symmetry 119
7.2.2 sigma-Model 121
7.2.3 NambuJonaLasinio Model 129
Part IV. Local Gauge Symmetries
8. Gauge Field Theories 135
8.1 Conserved Currents in QED 135
8.2 Local Abelian Gauge Invariance 137
8.3 Non-Abelian Gauge Fields 139
8.3.1 Lagrangian for Non-Abelian Gauge Field Theories 139
8.3.2 Properties of Non-Abelian Gauge Field Theories 144
9. Spontaneous Symmetry Breaking in Gauge Field Theories 147
9.1 Higgs Mechanism 147
9.2 Spontaneous Breaking of a Local Non-Abelian Symmetry 150
9.3 Summary of the Higgs Mechanism 155
Part V. Electroweak Interaction
10. Weak Interactions of Quarks and Leptons 159
10.1 Phenomenological Introduction 159
10.1.1 Strangeness Changing Weak Decays 159
10.1.2 Neutral Currents 160
10.2 Intermediate Vector Bosons 161
10.3 Fundamentals of a Theory of Weak Interactions 164
11. Electroweak Interactions of Leptons 167
11.1 Leptonic Multiplets and Interactions 167
11.1.1 Electroweak Currents 174
11.2 Lepton Masses 175
11.3 Electroweak Interactions 176
11.3.1 Generalization to Other Leptons 180
11.4 Parameters of the Lagrangian 180
11.4.1 Charged Current Experiments 180
11.4.2 Neutral Current Experiments 182
12. Electroweak Interactions of Quarks 187
12.1 Hadronic Multiplets 187
12.1.1 Hadron Masses 190
13. Electroweak Interactions of Quarks and Leptons 193
13.1 Lagrangian of Electroweak Interactions 193
13.2 Standard Model 194
14. CP Invariance of Electroweak Interactions 197
14.1 KobayashiMaskawa Matrix 197
14.2 Unitarity of the KM Matrix 198
14.3 K^0 Decay and CP Violation 201
14.4 CP Invariance and the KM Matrix 203
Part VI. Strong Interaction
15. Quantum Chromodynamics 209
15.1 Gauge Group for Strong Interactions 209
15.2 QCD Lagrangian 211
15.3 Properties of QCD 213
15.3.1 Scale Invariance 213
15.3.2 Chiral Invariance 214
15.3.3 Antishielding and Confinement 215
15.3.4 Deconfinement Phase Transition 217
Part VII. Hadron Structure
16. Bag Models of Hadrons 223
16.1 Potential Well in the Dirac Theory 223
16.2 The MIT Bag 228
16.2.1 Fermions in the MIT Bag 229
16.2.2 Hadron Masses 232
16.2.3 Gluons in the MIT Bag 234
16.2.4 Hyperfine Structure of Bag States 235
16.2.5 Magnetic Moments of the Nucleon 243
16.2.6 Axial Vector Current 246
16.2.7 Chiral Symmetry in the MIT Bag 251
17. Soliton Models of Hadrons 257
17.1 Skyrmion Model 258
17.2 Hybrid Chiral Bag Model 262
17.3 Linear sigma-Model 269
17.4 FriedbergLee Soliton Bag Model 272
17.5 NJL Soliton Model 274
Part VIII. Appendices
A. Solutions of the Free Dirac Equation 279
A.1 Properties of Free Dirac States 279
A.2 Massless Fermions 284
A.3 Dirac and Majorana Fields 286
B. Explicit Quark States for Hadrons 289
C. Table of Hadron Properties 293
Bibliography by Subject 297
References 303
Index 307
END
