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# Fields, Symmetries, and Quarks

### Theoretical and Mathematical Physics

Hardcover Published: 18th February 1999
ISBN: 9783540652359
Number Of Pages: 310

### Hardcover

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This revised and extended edition of the book Fields, Symmetries, and Quarks, originally published by McGraw-Hill Book Company, Hamburg, 1989, contains a new chapter on electroweak interactions which has also grown out of lectures that I have given in the meantime. In addition, a number of changes, mainly in the metric used, in the discussion of the theory of strong interactions, QCD, and in the chapter on hadron physics, have been made and errors have been corrected. The motivation for this book, however, is still the same as it was 10 years ago: This is a book on quantum field theory and our present understanding of leptons and hadrons for advanced students and the non-specialists and, in particular, the experimentalists working on problems of nuclear and hadron physics. I am grateful to Dr. S. Leupold for a very careful reading of the revised manuscript, many corrections, and helpful suggestions and to C. Traxler for producing the figures and for constructive discussions.

 Preliminaries Units and Metric p. 3 Units p. 3 Metric and Notation p. 4 Fundamentals of Field Theory Classical Fields p. 9 Equations of Motion p. 9 Examples p. 11 Symmetries and Conservation Laws p. 14 Geometrical Space-Time Symmetries p. 15 Internal Symmetries p. 17 Free Fields and Their Quantization p. 21 Classification of Fields p. 21 Scalar Fields p. 23 Quantization of the Hermitian Scalar Field p. 24 Quantization of the Charged Scalar Field p. 27 Vector Fields p. 29 Massive Vector Fields p. 29 Massless Vector Fields p. 30 Fermion Fields p. 32 Dirac Equation p. 32 Lagrangian for Fermion Fields p. 34 Quantization ofthe Dirac Field p. 35 Massless Fermions p. 38 Neutrinos p. 40 Transition Rates in Quantum Field Theory p. 44 Quantum Mechanical Consistency p. 52 GlobalSymmetries Symmetries of Meson and Baryon Systems p. 57 U(1) Symmetry p. 57 Properties of the Group U(1) p. 58 Structure of the Nucleon Lagrangian p. 59 SU(2) Symmetry p. 60 Properties of the Group SU(2) p. 60 General Definitions p. 64 Application to the Pion-Nucleon System p. 64 Structure of SU(2) Multiplets p. 72 SU(3) Symmetry p. 74 Properties of the Group SU(3) p. 75 Structure of SU(3) Multiplets p. 78 Assignments of Hadrons to SU(3) Multiplets p. 83 SU(3) Symmetry Breaking p. 85 Quarks p. 87 Construction of SU(3) Multiplets p. 87 Construction of the Representation <$>3 \otimes \bar {3}<$> p. 89 Construction of the Representation 3 ⊗ 3 ⊗ 3 p. 90 State Vectors for the Multiplets p. 92 Tensor Algebra p. 93 Hadron Multiplets p. 96 Color Degree of Freedom p. 100 Chiral Symmetry p. 103 Phenomenology of ß-Decay p. 103 Leptonic ß-Decay p. 103 Semileptonic ß-Decay p. 104 Current Conservation in Strong Interactions p. 106 Vector Current Conservation p. 106 Axial Vector Current Conservation p. 108 Chiral Symmetry Group p. 110 Chiral Symmetry Transformations for the Fermions p. 110 Chiral Symmetry Transformations for the Mesons p. 112 Spontaneous Global Symmetry Breaking p. 115 Goldstone Theorem p. 115 Goldstone Bosons p. 116 Examples of the Goldstone Mechanism p. 119 Spontaneous Breaking of a Global Non-Abelian Symmetry p. 119 ¿-Model p. 121 Nambu-Jona-Lasinio Model p. 129 Local Gauge Symmetries Gauge Field Theories p. 135 Conserved Currents in QED p. 135 Local Abelian Gauge Invariance p. 137 Non-Abelian Gauge Fields p. 139 Lagrangian for Non-Abelian Gauge Field Theories p. 139 Properties of Non-Abelian Gauge Field Theories p. 144 Spontaneous Symmetry Breaking in Gauge Field Theories p. 147 Higgs Mechanism p. 147 Spontaneous Breaking of a Local Non-Abelian Symmetry p. 150 Summary of the Higgs Mechanism p. 155 Electroweak Interaction Weak Interactions of Quarks and Leptons p. 159 Phenomenological Introduction p. 159 Strangeness Changing Weak Decays p. 159 Neutral Currents p. 160 Intermediate Vector Bosons p. 161 Fundamentals of a Theory of Weak Interactions p. 164 Electroweak Interactions of Leptons p. 167 Leptonic Multiplets and Interactions p. 167 Electroweak Currents p. 174 Lepton Masses p. 175 Electroweak Interactions p. 176 Generalization to Other Leptons p. 180 Parameters of the Lagrangian p. 180 Charged Current Experiments p. 180 Neutral Current Experiments p. 182 Electroweak Interactions of Quarks p. 187 Hadronic Multiplets p. 187 Hadron Masses p. 190 Electroweak Interactions of Quarks and Leptons p. 193 Lagrangian of Electroweak Interactions p. 193 Standard Model p. 194 CP Invariance of Electroweak Interactions p. 197 Kobayashi-Maskawa Matrix p. 197 Unitarity of the KM Matrix p. 198 K0 Decay and CP Violation p. 201 CP Invariance and the KM Matrix p. 203 Strong Interaction Quantum Chromodynamics p. 209 Gauge Group for Strong Interactions p. 209 QCD Lagrangian p. 211 Properties of QCD p. 213 Scale Invariance p. 213 Chiral Invariance p. 214 Antishielding and Confinement p. 215 Deconfinement Phase Transition p. 217 Hadron Structure Bag Models of Hadrons p. 223 Potential Well in the Dirac Theory p. 223 The MIT Bag p. 228 Fermions in the MIT Bag p. 229 Hadron Masses p. 232 Gluons in the MIT Bag p. 234 Hyperfine Structure of Bag States p. 235 Magnetic Moments of the Nucleon p. 243 Axial Vector Current p. 246 Chiral Symmetry in the MIT Bag p. 251 Soliton Models of Hadrons p. 257 Skyrmion Model p. 258 Hybrid Chiral Bag Model p. 262 Linear 7-Model p. 269 Friedberg-Lee Soliton Bag Model p. 272 NJL Soliton Model p. 274 Appendices Solutions of the Free Dirac Equation p. 279 Properties of Free Dirac States p. 279 Massless Fermions p. 284 Dirac and Majorana Fields p. 286 Explicit Quark States for Hadrons p. 289 Table of Hadron Properties p. 293 Bibliography by Subject p. 297 References p. 303 Index p. 307 Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9783540652359
ISBN-10: 3540652353
Series: Theoretical and Mathematical Physics
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 310
Published: 18th February 1999
Publisher: SPRINGER VERLAG GMBH
Country of Publication: DE
Dimensions (cm): 24.16 x 16.33  x 2.31
Weight (kg): 0.6
Edition Number: 2
Edition Type: Revised