An Introduction to Elementary Particles

ContentsPrefaceI. 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 ReferencesVI. 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 ReferencesVIII. 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- ReferencesIX. 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 ReferencesXI. 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 ReferencesXIV. 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 ReferencesAppendix A Functions of a Complex Variable A.l Functions and Singularities A.2 Integral Theorems ReferencesAppendix 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