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Fields, Symmetries, and Quarks : Theoretical and Mathematical Physics - Ulrich Mosel

Fields, Symmetries, and Quarks

Theoretical and Mathematical Physics


Published: 18th February 1999
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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.

Units and Metricp. 3
Unitsp. 3
Metric and Notationp. 4
Fundamentals of Field Theory
Classical Fieldsp. 9
Equations of Motionp. 9
Examplesp. 11
Symmetries and Conservation Lawsp. 14
Geometrical Space-Time Symmetriesp. 15
Internal Symmetriesp. 17
Free Fields and Their Quantizationp. 21
Classification of Fieldsp. 21
Scalar Fieldsp. 23
Quantization of the Hermitian Scalar Fieldp. 24
Quantization of the Charged Scalar Fieldp. 27
Vector Fieldsp. 29
Massive Vector Fieldsp. 29
Massless Vector Fieldsp. 30
Fermion Fieldsp. 32
Dirac Equationp. 32
Lagrangian for Fermion Fieldsp. 34
Quantization ofthe Dirac Fieldp. 35
Massless Fermionsp. 38
Neutrinosp. 40
Transition Rates in Quantum Field Theoryp. 44
Quantum Mechanical Consistencyp. 52
Symmetries of Meson and Baryon Systemsp. 57
U(1) Symmetryp. 57
Properties of the Group U(1)p. 58
Structure of the Nucleon Lagrangianp. 59
SU(2) Symmetryp. 60
Properties of the Group SU(2)p. 60
General Definitionsp. 64
Application to the Pion-Nucleon Systemp. 64
Structure of SU(2) Multipletsp. 72
SU(3) Symmetryp. 74
Properties of the Group SU(3)p. 75
Structure of SU(3) Multipletsp. 78
Assignments of Hadrons to SU(3) Multipletsp. 83
SU(3) Symmetry Breakingp. 85
Quarksp. 87
Construction of SU(3) Multipletsp. 87
Construction of the Representation <$>3 \otimes \bar {3}<$>p. 89
Construction of the Representation 3 ⊗ 3 ⊗ 3p. 90
State Vectors for the Multipletsp. 92
Tensor Algebrap. 93
Hadron Multipletsp. 96
Color Degree of Freedomp. 100
Chiral Symmetryp. 103
Phenomenology of ß-Decayp. 103
Leptonic ß-Decayp. 103
Semileptonic ß-Decayp. 104
Current Conservation in Strong Interactionsp. 106
Vector Current Conservationp. 106
Axial Vector Current Conservationp. 108
Chiral Symmetry Groupp. 110
Chiral Symmetry Transformations for the Fermionsp. 110
Chiral Symmetry Transformations for the Mesonsp. 112
Spontaneous Global Symmetry Breakingp. 115
Goldstone Theoremp. 115
Goldstone Bosonsp. 116
Examples of the Goldstone Mechanismp. 119
Spontaneous Breaking of a Global Non-Abelian Symmetryp. 119
¿-Modelp. 121
Nambu-Jona-Lasinio Modelp. 129
Local Gauge Symmetries
Gauge Field Theoriesp. 135
Conserved Currents in QEDp. 135
Local Abelian Gauge Invariancep. 137
Non-Abelian Gauge Fieldsp. 139
Lagrangian for Non-Abelian Gauge Field Theoriesp. 139
Properties of Non-Abelian Gauge Field Theoriesp. 144
Spontaneous Symmetry Breaking in Gauge Field Theoriesp. 147
Higgs Mechanismp. 147
Spontaneous Breaking of a Local Non-Abelian Symmetryp. 150
Summary of the Higgs Mechanismp. 155
Electroweak Interaction
Weak Interactions of Quarks and Leptonsp. 159
Phenomenological Introductionp. 159
Strangeness Changing Weak Decaysp. 159
Neutral Currentsp. 160
Intermediate Vector Bosonsp. 161
Fundamentals of a Theory of Weak Interactionsp. 164
Electroweak Interactions of Leptonsp. 167
Leptonic Multiplets and Interactionsp. 167
Electroweak Currentsp. 174
Lepton Massesp. 175
Electroweak Interactionsp. 176
Generalization to Other Leptonsp. 180
Parameters of the Lagrangianp. 180
Charged Current Experimentsp. 180
Neutral Current Experimentsp. 182
Electroweak Interactions of Quarksp. 187
Hadronic Multipletsp. 187
Hadron Massesp. 190
Electroweak Interactions of Quarks and Leptonsp. 193
Lagrangian of Electroweak Interactionsp. 193
Standard Modelp. 194
CP Invariance of Electroweak Interactionsp. 197
Kobayashi-Maskawa Matrixp. 197
Unitarity of the KM Matrixp. 198
K0 Decay and CP Violationp. 201
CP Invariance and the KM Matrixp. 203
Strong Interaction
Quantum Chromodynamicsp. 209
Gauge Group for Strong Interactionsp. 209
QCD Lagrangianp. 211
Properties of QCDp. 213
Scale Invariancep. 213
Chiral Invariancep. 214
Antishielding and Confinementp. 215
Deconfinement Phase Transitionp. 217
Hadron Structure
Bag Models of Hadronsp. 223
Potential Well in the Dirac Theoryp. 223
The MIT Bagp. 228
Fermions in the MIT Bagp. 229
Hadron Massesp. 232
Gluons in the MIT Bagp. 234
Hyperfine Structure of Bag Statesp. 235
Magnetic Moments of the Nucleonp. 243
Axial Vector Currentp. 246
Chiral Symmetry in the MIT Bagp. 251
Soliton Models of Hadronsp. 257
Skyrmion Modelp. 258
Hybrid Chiral Bag Modelp. 262
Linear 7-Modelp. 269
Friedberg-Lee Soliton Bag Modelp. 272
NJL Soliton Modelp. 274
Solutions of the Free Dirac Equationp. 279
Properties of Free Dirac Statesp. 279
Massless Fermionsp. 284
Dirac and Majorana Fieldsp. 286
Explicit Quark States for Hadronsp. 289
Table of Hadron Propertiesp. 293
Bibliography by Subjectp. 297
Referencesp. 303
Indexp. 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
Country of Publication: DE
Dimensions (cm): 24.16 x 16.33  x 2.31
Weight (kg): 0.6
Edition Number: 2
Edition Type: Revised