# Current Algebras and Their Applications

## 1st Edition

### International Series of Monographs in Natural Philosophy

**Authors:**B. Renner

**Editors:**D. ter Haar

**eBook ISBN:**9781483184135

**Imprint:**Pergamon

**Published Date:**1st January 1968

**Page Count:**192

## Description

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.

## Table of Contents

Foreword

Preface

1. Preliminary Concepts

1.1. The Interactions of Subnuclear Particles

1.2. The Isospin Symmetry of Strong Interactions

1.3. The SU3-Symmetry Model

1.4. Quarks and the SUe-Model

2. The Basic Ideas of Current Algebras

2.1. Current Commutators

2.2. The SU3 x SU3 Algebra

2.3. A Quark Model for the SU3 x SU3 Algebra

2.4. Lepton Scattering Sum Rules

2.5. Some Remarks on the Mathematical Description of Currents and Charges

3. Approximate SU3 Symmetry in Current Algebra Theory

3.1. The Description of an Approximate Symmetry

3.2. The Momentum Dependence of Direct Sum Rules

3.3. Corrections to SU3 Results

4. The Dispersion Theory of Current Algebras, I

4.1. A Covariant Derivation of Sum Rules

4.2. The Relationship between Direct Sum Rules and Dispersion Sum Rules

4.3. Sum Rules for Vertex Functions

5. Current Algebra Sum Rules with PCAC

5.1. The Principle of PCAC or Pion Pole dominance

5.2. The Adler-Weisberger Relation

5.3. Generalized Adler-Weisberger Relations

5.4. A Photoproduction Sum Rule for the Nucleon Magnetic Moments

5.5. On the Existence of Axial Vector Mesons

6. Low-Energy Theorems

6.1. General Considerations

6.2. The K-meson Leptonic Decays

6.3. Scattering Lengths of Mesons

6.4. Vector Meson Decays

6.5. Non-Leptonic Weak Decays

7. Extensions of the SU3xSU3 Current Algebra

7.1. The Chiral SU6 X SU6 Algebra

7.2. The Connections of the Static SU6 Algebra with SU3XSU3

7.3. The Baryon Magnetic Moments and Mixing Schemes

7.4. The U12 Current Algebra

7.5. Other Extensions

8. Schwinger Terms

8.1. The Existence of Schwinger Terms

8.2. Alternative Approaches to Schwinger Terms

9. The Dispersion Theory of Current Algebras, II

9.1. The Dispersion Theory of Local Current Commutators

9.2. General Sum Rules for Spinless Particles

9.3. The Sum Rule of Cabibbo and Radicati

9.4. Sum Rules for Finite Momentum Transfer, Superconvergence Relations

9.5. On the Asymptotic Behaviour of Current Commutator Matrix Elements

9.6. Other Classes of Dispersion Sum Rules

10. Possible Connections of Current Algebras and Dynamics

Appendix. Some Details in LSZ Reduction Formulae Conventions

Bibliography on Current Algebras

Selected General References

Index

## Details

- No. of pages:
- 192

- Language:
- English

- Copyright:
- © Pergamon 1968

- Published:
- 1st January 1968

- Imprint:
- Pergamon

- eBook ISBN:
- 9781483184135