# An Introduction to Elementary Particles

## 2nd Edition

**Authors:**W.S.C. Williams

**eBook ISBN:**9780323161596

**Imprint:**Academic Press

**Published Date:**1st January 1971

**Page Count:**544

## Description

An Introduction to Elementary Particles, Second Edition aims to give an introduction to the theoretical methods and ideas used to describe how elementary particles behave, as well as interpret some of the phenomena associated with it. The book covers topics such as quantum mechanics; brats, kets, vectors, and linear operations; angular momentum; scattering and reaction theory; the polarization and angularization of spin-0-spin-1/2 scattering; and symettery, isotopic spin, and hypercharge. The book also discusses particles such as bosons, baryons, mesons, kaons, and hadrons, as well as the interactions between them. The text is recommended for physicists, especially those who are practitioners and researchers in the fields of quantum physics and elementary-particle physics.

## Table of Contents

Contents

Preface

I. Quantum Mechanics

1.1 Introduction

1.2 Bras, Kets, Vectors, and Linear Operators

1.3 Quantum Mechanics

1.4 Time Development of Vectors

1.5 The Lorentz Transformations

1.6 Transformations

1.7 Parity, the Parity Transformation, and Parity Conservation

1.8 Center-of-Mass and Laboratory Coordinates

1.9 Conclusions

References

II. Angular Momentum

2.1 Introduction

2.2 Orbital Angular Momentum

2.3 Rotations (I)

2.4 Spin and Total Angular Momentum

2.5 The Eigenvalues of Angular Momentum

2.6 The Matrix Elements of Angular Momentum

2.7 Vector Addition of Angular Momentum

2.8 The Eigenfunctions of Orbital Angular Momentum

2.9 The Pauli Spin Matrices

2.10 Rotations (II)

2.11 Decay of Pure States

2.12 Tensor Operators

2.13 Polarization

2.14 The Density Matrix

2.15 Decay of Mixed Spin States

2.16 Rotation of the Density Matrix

References

III. Scattering and Reaction Theory

3.1 Introduction

3.2 The Partial-Wave Analysis

3.3 Scattering of Spin-0 by Spin-i Particles

3.4 Polarization in Spin-O-Spin-i Scattering

3.5 Angular Distributions in Spin-O-Spin-i Scattering

3.6 The Ambiguities of Spin-O-Spin-i Scattering

3.7 The Scattering of Spin-i by Spin-i Particles

3.8 The Scattering of Identical Particles

3.9 The Scattering Matrix (I)

3.10 Binary Reactions

3.11 The Scattering Matrix (II)

3.12 Reciprocity

3.13 The Principle of Detailed Balance

References

IV. Energy Dependence in Scattering

4.1 Introduction

4.2 Phase-Space Considerations

4.3 Phase Shifts at Low Energy

4.4 The Wigner Condition

4.5 Resonance and the Breit-Wigner Formula

4.6 Unitarity

References

V. Symmetry, Isotopic Spin, and Hypercharge

5.1 Introduction

5.2 Symmetry and Antisymmetry

5.3 Two-Nucleon State Vectors

5.4 Isotopic Spin

5.5 Strangeness and Hypercharge

5.6 Conclusion

References

VI. Parity, Time Reversal, Charge Conjugation, and G-Parity

6.1 Introduction

6.2 Parity

6.3 Parity Conservation

6.4 Parity Nonconservation

6.5 Time Reversal

6.6 The Consequences of Time-Reversal Invariance

6.7 Charge Conjugation

6.8 G-Parity

6.9 The CPT Theorem

9.10 Conclusion

References

VII. The Bosons

7.1 Introduction

7.2 The Pions

7.3 The Spin and Parity of the Pions

7.4 The ^-Mesons

7.5 The Neutral tf-Meson System

7.6 Meson Resonances

7.7 Meson Resonances Decaying into Two Mesons

7.8 Meson Resonances Decaying into Three Mesons (I)

7.9 Meson Resonances Decaying into Three Mesons (II)

7.10 Conclusion

References

VIII. The Baryons

8.1 Introduction

8.2 The Stable Baryons

8.3 Baryon Resonances

8.4 Isotopic Spin of the Pion-Nucleon System

8.5 Low-Energy Pion-Nucleon Scattering

8.6 Pion-Nucleon Scattering up to 2500 MeV

8.7 The Kaon-Nucleon System

8.8 Low-Energy Kaon-Nucleon Scattering

8.9 The Antikaon-Nucleon System

8.10 The Production of Baryon Resonances

8.11 Ω-

References

IX. Unitary Symmetry

9.1 Introduction

9.2 Symmetry and the Classification of States

9.3 The Theory of Continuous Groups

9.4 The Hadrons and SU(3) Multiplets

9.5 Properties of Representation

9.6 Applications of SU(3)

9.7 Applications of Broken SU(3)

9.8 Quarks

9.9 Higher Symmetry Schemes

9.10 Conclusion

References

X. Field Theory

10.1 Introduction

10.2 First Quantization

10.3 Units and Notation

10.4 The Lagrangian Formalism

10.5 The Electromagnetic Field

10.6 The Dirac Field

10.7 Second Quantization and the Commutation Relations

10.8 Interaction and the S-Matrix

10.9 Renormalization and the Radiative Corrections

10.10 QED at High Energies

10.11 Field Theory and Strong Interactions

10.12 Conclusion

References

XI. Weak Interactions

11 .1 Introduction

11 .2 The Description and Theory of Beta Decay

11 .3 The Classification of Beta Decays

11 .4 Beta Decay: Pre-1956

11 .5 Beta Decay: Post-1956

11 .6 The Two-Component Theory of the Neutrino

11 .7 Conservation of Leptons in Beta Decay

11 .8 Muon and Pion Decay

11 .9 The Universal Weak Interaction

11 .10 The Conserved Vector Current

11 .11 Muon Capture

11 .12 The Leptonic Decays of Strange Particles

11 .13 The Cabibbo Angle

11 .14 The Nonleptonic Decay of Strange Particles

11 .15 The Intermediate Vector Boson

11 .16 Neutrino Interactions

11 .17 Conclusion

References

XII. Strong Interactions

12.1 Introduction

12.2 The Mandelstam Variables

12.3 The Analytic Properties of the S-Matrix

12.4 Pion-Nucleon Scattering Dispersion Relations

12.5 Other Singularities

12.6 Strong Interactions at High Energies

12.7 Asymptotic Relations

12.8 One-Particle-Exchange Mechanisms

12.9 Regge Poles

12.10 The Chew-Frautschi Plot

References

XIII. The Electromagnetic Interaction of Hadrons

13.1 Introduction

13.2 The Electromagnetic Interaction

13.3 Isotopic-Spin Selection Rules

13.4 The Angular-Momentum Properties of the Electromagnetic Field

13.5 Photoproduction Processes

13.6 Electromagnetic Form Factors

13.7 The Vector-Dominance Model

References

XIV. The Neutral Kaons and CP Conservation

14.1 Introduction

14.2 The Time Development of Neutral-Kaon Systems

14.3 The Neutral-Kaon Mass Difference

14.4 The Theory of Regeneration

14.5 The Sign of the Mass Difference

14.6 CP Nonconservation

14.7 CP Noninvariant Analysis

14.8 The Experimental Situation

14.9 The Source of CP Violation

References

Appendix A Functions of a Complex Variable

A.l Functions and Singularities

A.2 Integral Theorems

References

Appendix Β Relativistic Kinematics

B.l The Properties of Four Vectors

B.2 Laboratory and Center-of-Mass Coordinates

B.3 Particle Reactions

B.4 Dalitz Plots

B.5 The Mandelstam Variables

B.6 Transformation of Differential Cross Sections

B.7 Transformation of the Polarization Vector

References

Appendix C Phase Space

C.l The Density-of-States Factor

C.2 Phase Space and Dalitz Plots

References

Appendix D Dirac Matrix Elements

D.l The Structure of Matrix Elements for Dirac Particles

Reference

Appendix Ε Tables of Clebsch-Gordan Coefficients and of Rotation Matrix Elements

E.l Clebsch-Gordan Coefficients

E.2 Rotation Matrix Elements

References

Author Index

Subject Index

## Details

- No. of pages:
- 544

- Language:
- English

- Copyright:
- © Academic Press 1971

- Published:
- 1st January 1971

- Imprint:
- Academic Press

- eBook ISBN:
- 9780323161596