Renner / Ter Haar Current Algebras and Their Applications

International Series of Monographs in Natural Philosophy
1. Auflage 2014
ISBN: 978-1-4831-8413-5
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 192 Seiten, Web PDF

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.

Autoren/Hrsg.

Renner, B.

Ter Haar, D.

Inhaltsverzeichnis

1;Front Cover;1
2;Current Algebras and Their Applications;4
3;Copyright Page;5
4;Table of Contents;8
5;Dedication;6
6;Foreword;10
7;Preface;14
8;CHAPTER 1. Preliminary Concepts;16
8.1;1.1. The Interactions of Subnuclear Particles;16
8.2;1.2. The Isospin Symmetry of Strong Interactions;21
8.3;1.3. The SU3-Symmetry Model;25
8.4;1.4. Quarks and the SU6-Model;30
9;CHAPTER 2. The Basic Ideas of Current Algebras;34
9.1;2.1. Current Commutators;34
9.2;2.2. The SU3 x SU3 Algebra;37
9.3;2.3. A Quark Model for the SU3 x SU3 Algebra;40
9.4;2.4. Lepton Scattering Sum Rules;42
9.5;2.5. Some Remarks on the Mathematical Description of Currents and Charges;47
10;CHAPTER 3. Approximate SIX Symmetry in Current Algebra Theory;49
10.1;3.1. The Description of an Approximate Symmetry;49
10.2;3.2. The Momentum Dependence of Direct Sum Rules;53
10.3;3.3. Corrections to SU3 Results;56
11;CHAPTER 4. The Dispersion Theory of Current Algebras, I;59
11.1;4.1. A Covariant Derivation of Sum Rules;59
11.2;4.2. The Relationship between Direct Sum Rules and Dispersion Sum
Rules;64
11.3;4.3. Sum Rules for Vertex Functions;72
12;CHAPTER 5. Current Algebra Sum Rules with PCAC;74
12.1;5.1. The Principle of PCAC or Pion Pole Dominance;74
12.2;5.2. The Adler-Weisberger Relation;77
12.3;5.3. Generalized Adler-Weisberger Relations;81
12.4;5.4. A Photoproduction Sum Rule for the Nucléon Magnetic Moments;86
12.5;5.5. On the Existence of Axial Vector Mesons;91
13;CHAPTER 6. Low-Energy Theorems;94
13.1;6.1. General Considerations;94
13.2;6.2. The K-meson Leptonic Decays;98
13.3;6.3. Scattering Lengths of Mesons;101
13.4;6.4. Vector Meson Decays;106
13.5;6.5. Non-leptonic Weak Decays;110
14;CHAPTER 7. Extensions of the SU3 . SU3 Current Algebra;119
14.1;7.1. The Chiral SU6 x SU6 Algebra;119
14.2;7.2. The Connections of the Static SU6 Algebra with SU3 x SU3;122
14.3;7.3. The Baryon Magnetic Moments and Mixing Schemes;125
14.4;7.4. The U12 Current Algebra;129
14.5;7.5. Other Extensions;132
15;CHAPTER 8. Schwinger Terms;133
15.1;8.1. The Existence of Schwinger Terms;133
15.2;8.2. Alternative Approaches to Schwinger Terms;137
16;CHAPTER 9. The Dispersion Theory of Current Algebras, II;140
16.1;9.1. The Dispersion Theory of Local Current Commutators;140
16.2;9.2. General Sum Rules for Spinless Particles;144
16.3;9.3. The Sum Rule of Cabibbo and Radicati;148
16.4;9.4. Sum Rules for Finite Momentum Transfer, Superconvergence
Relations;152
16.5;9.5. On the Asymptotic Behaviour of Current Commutator Matrix Elements;155
16.6;9.6. Other Classes of Dispersion Sum Rules;160
17;CHAPTER 10. Possible Connections of Current Algebras and Dynamics;166
18;APPENDIX: Some Details on LSZ Reduction Formulae;168
19;Conventions;172
20;Bibliography on Current Algebras;174
21;Selected General References;188
22;Index;190