Introduction to Elementary Particle Theory - 1st Edition - ISBN: 9780080179544, 9781483187310

Introduction to Elementary Particle Theory

1st Edition

International Series of Monographs In Natural Philosophy

Authors: Yu. V. Novozhilov
Editors: D. ter Haar
eBook ISBN: 9781483187310
Imprint: Pergamon
Published Date: 1st January 1975
Page Count: 400
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Introduction to Elementary Particle Theory details the fundamental concepts and basic principles of the theory of elementary particles. The title emphasizes on the phenomenological foundations of relativistic theory and to the strong interactions from the S-matrix standpoint. The text first covers the basic description of elementary particles, and then proceeds to tackling relativistic quantum mechanics and kinematics. Next the selection deals with the problem of internal symmetry. In the last part, the title details the elements of dynamical theory. The book will be of great use to students and researchers in the field of particle physics.

Table of Contents


Author's Preface to the English Edition

Translator's Preface


Part I Introduction: States of Elementary Particles

Chapter 1. Elements of Relativistic Quantum Theory

§ 1.1. Homogeneity of Space-time and the Poincare Group

§ 1.2. Quantum Mechanics and Relativity

§ 1.3. Basis Quantities

§ 1.4. Description of Scattering. The S-matrix

Chapter 2. Foundations of Phenomenological Description

§ 2.1. Interactions and Internal Symmetry

§ 2.2. Symmetry and Particle Classification

§ 2.3. Unstable Particles

Part II Relativistic Kinematics and Reflections

Chapter 3. The Lorentz Group and the Group SL(2,c)

§ 3.1. Second-order Unimodular Matrices and the Lorentz Transformation

§ 3.2. Spinors

§ 3.3. Irreducible Representations and Generalized Spinor Analysis

§ 3.4. Direct Products of Representations and Covariant Clebsch-Gordan Coefficients

§ 3.5. Representations of the Unitary Group SU2

Chapter 4. The Quantum Mechanical Poincare Group

§ 4.1. Introductory Remarks

§ 4.2. Transformations and Momenta. The Little Group and the Wigner Operator

§ 4.3. Unitary Representations. Case m²>0

§ 4.4. Spinor Functions and Quantum Fields for m²>0

§ 4.5. Unitary Representations in the Case m = 0. Equations of Motion

§ 4.6. Multi-particle States

Chapter 5. Wave Functions and Equations of Motion for Particles with Arbitrary Spin

§ 5.1. Wave Functions, Bilinear Hermitian Forms, and Equations of Motion

§ 5.2. The Dirac Equation

§ 5.3. 2(2J+l)-Component Wave Functions for Spin J

§ 5.4. Particles with Spin J = 1

§ 5.5. Rarita-Schwinger Wave Functions

§ 5.6. Bargmann-Wigner Wave Functions

§ 5.7. The Duffin-Kemmer Equation

Chapter 6. Reflections

§ 6.1. Total Reflection Θ, or CPT

§ 6.2. The operations P, C, and Τ

§ 6.3. Reflections and Interactions. Decays

§ 6.4. Summary of Formula for Reflection Transformations

Chapter 7. The Scattering Matrix. Kinematics

§ 7.1. The Problem of Kinematics

§ 7.2. The Variables s, t, u

§ 7.3. Cross-sections for Processes. Unitarity and Optical Theorem

§ 7.4. Helicity Amplitudes

§ 7.5. Spinor Amplitudes (m-functions) and Invariant Amplitudes

Part III Internal Symmetry

Chapter 8. Bospin Symmetry

§ 8.1. Isospin Multiplets, Hypercharge, and the Group SU2

§ 8.2. Isospin and Reflections. Antiparticle States. G-parity

§ 8.3. Multi-particle Dtates and Isospin Amplitudes. Decays and Relations between Reactions

Chapter 9. The Group SU3

§ 9.1. The Matrices λa and Structure Constants

§ 9.2 The fundamental Representation and Quarks. U- and V-spin

§ 9.3. Representations of the Group SU3

Chapter 10. SUs Symmetry and Classification of Particles and Resonances

§ 10.1. Unitary Representations and Multiplets

§ 10.2. Symmetry Breaking and Mass Splitting

§ 10.3. Relations between Transition Amplitudes

§ 10.4. The Quark Model

§ 10.5. SU6 Multiplets

Part IV Element of Dynamical Theory

Chapter 11. The S-matrix, Currents and Crossing Symmetry

§ 11.1. Interpolating Fields, Currents, and the Reduction Formula

§ 11.2. Crossing Symmetry

§ 11.3. Crossing matrices for SU2 and SU3

§ 11.4. Properties of Vertex Parts

Chapter 12. Analytic Properties of the Scattering Amplitude

§ 12.1. Unitarity and the Absorptive Part

§ 12.2. Maximal Analyticity

§ 12.3. Dispersion Relations

§ 12.4. Partial Wave Amplitudes and Fixed-energy Dispersion Relations. The Gribov-Froissart Formula

§ 12.5. Analytic Properties of Form Factors. The Pion Form Factor

Chapter 13. Asymptotic Behavior of the Scattering Amplitude at High Energies. Regge Poles

§ 13.1. Scattering at High Energies (Experiment)

§ 13.2. Bounds on the Amplitude at High Energies

§ 13.3. The Regge-pole Hypothesis and the aAymptotic Form of the Amplitude

§ 13.4. Simplest Consequences of the Regge-pole Hypothesis. The Diffraction Peak and the Total Cross-section

§ 13.5. Properties of Regge Trajectories

Chapter 14. Duality and the Yeneziano Model

§ 14.1. Finite Energy Sum Rules

§ 14.2. Duality. Duality Diagrams

§ 14.3. The Veneziano Model

§ 14.4. Some Applications of the Veneziano Model

Chapter 15. Electromagnetic and Weak Currents. Current Algebra

§ 15.1. Electromagnetic and Weak Currents

§ 15.2. The Gell-Mann Algebra of Densities and Charges. The Groups SU2XSU2 and SU3XSU3

§ 15.3. Partial Conservation of Axial Current

§ 15.4. Renormalization of the Axial Vector Coupling Constant

§ 15.5. Asymptotic Chiral Symmetry and Spectral Sum Rules

§ 15.6. Violation of CP Invariance




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© Pergamon 1975
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About the Author

Yu. V. Novozhilov

About the Editor

D. ter Haar

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