Current Algebras and Their Applications (eBook)

International Series of Monographs in Natural Philosophy

B. Renner (Autor)

D. ter Haar (Herausgeber)

eBook Download: PDF

2014 | 1. Auflage
192 Seiten
Elsevier Science (Verlag)
978-1-4831-8413-5 (ISBN)

Infos

International Series of Monographs in Natural Philosophy, Volume 12: Current Algebras and their Applications provides an introduction to the underlying philosophy and to the technical methods associated with the use of the Current Algebra for the investigation of questions in elementary particle physics. This text contains 10 chapters and begins with the preliminary concepts and basic ideas of current algebras. The next chapters deal with the approximate symmetry and the dispersion theory of current algebras, as well as the current algebra sum rules with PCAC. These topics are followed by reviews of the principles of the low-energy theorems, the Schwinger terms, and the features of the dispersion theory. The last chapter examines the possible connections of current algebras and dynamics. This book will prove useful to mathematicians, physicists, teachers, and students.

Inhalt

Front Cover 1
Current Algebras and Their Applications 4
Copyright Page 5
Table of Contents 8
Dedication 6
Foreword 10
Preface 14
CHAPTER 1. Preliminary Concepts 16
1.1. The Interactions of Subnuclear Particles 16
1.2. The Isospin Symmetry of Strong Interactions 21
1.3. The SU3-Symmetry Model 25
1.4. Quarks and the SU6-Model 30
CHAPTER 2. The Basic Ideas of Current Algebras 34
2.1. Current Commutators 34
2.2. The SU3 x SU3 Algebra 37
2.3. A Quark Model for the SU3 x SU3 Algebra 40
2.4. Lepton Scattering Sum Rules 42
2.5. Some Remarks on the Mathematical Description of Currents and Charges 47
CHAPTER 3. Approximate SIX Symmetry in Current Algebra Theory 49
3.1. The Description of an Approximate Symmetry 49
3.2. The Momentum Dependence of Direct Sum Rules 53
3.3. Corrections to SU3 Results 56
CHAPTER 4. The Dispersion Theory of Current Algebras, I 59
4.1. A Covariant Derivation of Sum Rules 59
4.2. The Relationship between Direct Sum Rules and Dispersion Sum 
64 
4.3. Sum Rules for Vertex Functions 72
CHAPTER 5. Current Algebra Sum Rules with PCAC 74
5.1. The Principle of PCAC or Pion Pole Dominance 74
5.2. The Adler-Weisberger Relation 77
5.3. Generalized Adler-Weisberger Relations 81
5.4. A Photoproduction Sum Rule for the Nucléon Magnetic Moments 86
5.5. On the Existence of Axial Vector Mesons 91
CHAPTER 6. Low-Energy Theorems 94
6.1. General Considerations 94
6.2. The K-meson Leptonic Decays 98
6.3. Scattering Lengths of Mesons 101
6.4. Vector Meson Decays 106
6.5. Non-leptonic Weak Decays 110
CHAPTER 7. Extensions of the SU3 . SU3 Current Algebra 119
7.1. The Chiral SU6 x SU6 Algebra 119
7.2. The Connections of the Static SU6 Algebra with SU3 x SU3 122
7.3. The Baryon Magnetic Moments and Mixing Schemes 125
7.4. The U12 Current Algebra 129
7.5. Other Extensions 132
CHAPTER 8. Schwinger Terms 133
8.1. The Existence of Schwinger Terms 133
8.2. Alternative Approaches to Schwinger Terms 137
CHAPTER 9. The Dispersion Theory of Current Algebras, II 140
9.1. The Dispersion Theory of Local Current Commutators 140
9.2. General Sum Rules for Spinless Particles 144
9.3. The Sum Rule of Cabibbo and Radicati 148
9.4. Sum Rules for Finite Momentum Transfer, Superconvergence 
152 
9.5. On the Asymptotic Behaviour of Current Commutator Matrix Elements 155
9.6. Other Classes of Dispersion Sum Rules 160
CHAPTER 10. Possible Connections of Current Algebras and Dynamics 166
APPENDIX: Some Details on LSZ Reduction Formulae 168
Conventions 172
Bibliography on Current Algebras 174
Selected General References 188
Index 190

Produkt-Details

• Erscheint lt. Verlag: 20.6.2014
• Sprache: englisch
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Quantenphysik
• Themenwelt: Sozialwissenschaften ► Ethnologie
• Themenwelt: Sozialwissenschaften ► Politik / Verwaltung
• Themenwelt: Sozialwissenschaften ► Soziologie
• ISBN-10: 1-4831-8413-7 / 1483184137
• ISBN-13: 978-1-4831-8413-5 / 9781483184135