Elementary Particle Physics

I Relativistic Kinematics and Quantum Fields.- 1 Introduction.- 2 The Theory of Special Relativity and Relativistic Kinematics.- 2.1 The Basic Principles of Special Relativity.- 2.2 Energy and Momentum of Relativistic Particles.- 2.3 The Relativistic Kinematics of a Collision Between Two Particles.- Exercises.- 3 Particles and Fields.- 3.1 The Schrödinger, Dirac, and Heisenberg Pictures of Quantum Mechanics.- 3.2 Free Particles and the Fock Space.- 3.3 The Lagrange Formalism and the Noether Theorems.- 3.4 The Canonical Quantization Rules.- Exercises.- 4 The Dirac Equation and the Dirac Field.- 4.1 The Dirac Equation.- 4.2 Solutions of the Dirac Equation.- 4.3 Transformation Rules for the Dirac Field.- 4.4 Quantization and Interpretation of the Dirac Field.- 4.5 Parity, Charge-Conjugation, and Time-Reversal Invariance of the Free Dirac Field.- 4.5.1 The Parity Transformation P.- 4.5.2 The Charge-Conjugation Transformation C.- 4.5.3 The Time-Reversal Transformation T.- Exercises.- 5 The Scattering Matrix and the Scattering Cross-Section.- 5.1 The Scattering of Electrons by a Heavy Nucleus.- 5.2 General Definition of the S- and T-Matrix.- 5.3 The Unitary Relation and the Optical Theorem.- 5.4 The Decay Rate of an Unstable Particle.- Exercises.- II Quantum Electrodynamics.- 6 Introductory Remarks.- 7 The Quantization of the Free Electromagnetic Field.- 7.1 Commutation Rules and Indefinite Metric.- 7.2 Normal-Ordered and Time-Ordered Products.- Exercises.- 8 Further Aspects of the Theory of the Free Dirac Field.- 8.1 The Dirac Current.- 8.2 The Magnetic Moment of the Electron in the Dirac Theory.- 8.3 The Free Electron Propagator.- Exercises.- 9 Electromagnetic Coupling and the Perturbation Expansion.- 9.1 The Electromagnetic Coupling of the Dirac Field.- 9.2 The Feynman Rules.- Exercises.- 10 Simple Reactions in Quantum Electrodynamics.- 10.1 Electron–Electron Scattering (Møller Scattering).- 10.2 Electron–Positron Scattering (Bhabha Scattering).- 10.3 Compton Scattering.- Exercises.- 11 The Muon and Muon Pair Production in Electron–Positron Annihilation.- 11.1 Properties of the Muon.- 11.2 The Reaction e?e+ ? ???+.- Exercises.- 12 External Fields.- 12.1 The Scattering of Electrons in an External Potential.- 12.2 Bremsstrahlung.- 12.3 Pair Creation (The Bethe–Heitler Process).- Exercises.- 13 Positronium.- 13.1 The Spectrum of Positronium States and Their General Properties.- 13.2 The Decay of Positronium.- Exercises.- 14 Radiative Corrections.- 14.1 Radiative Corrections to the Scattering in an External Potential.- 14.2 The Lamb Shift.- III The Strong Interaction.- 15 Historical Overview.- 16 Phenomenology of Hadronic Reactions.- 16.1 Resonance Physics.- 16.2 A Basis for the Hadron States and the Symmetries C, P, and T.- 16.3 Partial Wave Analysis.- 16.4 Total Cross-Sections at High Energies.- 16.5 Multi-Particle Production at High Energies.- Exercises.- 17 Internal Symmetries of the Strong Interaction and the Quark Model.- 17.1 Mathematics of the SU(3) Group.- 17.2 The Quark Model and the Flavor-SU(3) Group.- 17.3 The Gell-Mann–Okubo Mass Formula.- 17.4 The SU(6) Symmetry.- Exercises.- 18 The Naïve Parton Model.- 18.1 Electron–Positron Annihilation into Hadrons.- 18.2 Deep Inelastic Lepton–Nucleon Scattering.- 18.3 The Flavor Quantum Numbers of the Partons.- 18.4 Sum Rules and Evidence for Flavor-Neutral Partons, Gluons.- 18.5 The Drell–Yan Process.- Exercises.- 19 The Basic Principles of Quantum Chromodynamics.- 19.1 The Lagrange Density of Quantum Chromodynamics (QCD).- 19.2 Violation of the Bjorken Scale Invariance in Deep Inelastic Scattering.- 19.3 The Calculation of Anomalous Dimensions in QCD.- 19.4 Comparison of Deep Inelastic Scattering Data with QCD.- Exercises.- 20 Jet and Quarkonium Physics.- 20.1 The Naïve Jet Model.- 20.2 Jets and QCD Effects in Electron–Positron Annihilation into Hadrons.- 20.3 Quarkonium.- 20.4 Jets in Hadron–Hadron Collisions.- Exercises.- IV The Electroweak Interaction.- 21 From ?-Decay to the W-Boson. A Historical Survey.- 21.1 The Early Days, the Neutrino Hypothesis, Four-Fermion Coupling.- 21.2 Parity Violation and the (V – A) Theory.- 21.3 The Universality of the Weak Interaction and the Cabibbo Theory.- 21.4 Neutral Currents, the W- and Z-Bosons, and the Glashow–Weinberg–Salam Theory.- Exercises.- 22 The Lagrange Densities of Quantum Flavor Dynamics and of the Standard Model.- 22.1 The Gauge Group of the Electroweak Interaction.- 22.2 The Higgs Field and Spontaneous Symmetry Breaking.- 22.3 The Extension of Quantum Flavor Dynamics to Other Leptons and to Quarks, and the Effective Lagrange Density at Low Energies.- 22.4 The Mass Matrix and the Cabibbo Angles.- 22.5 The Lagrange Density of the Standard Model.- Exercises.- 23 Decay Processes in the Standard Model and the Determination of the Quark Mixing Angles in the Charged Current.- 23.1 The Decay of the Muon.- 23.2 The Decay of the ?-Lepton.- 23.3 The ?-Decay of the Neutron and the Determination of the Kobayashi–Maskawa Matrix Element V11.- 23.4 Hyperon Decay Processes and the Determination of V12.- 23.5 The Decays of Charged Pions.- 23.6 The Decay of Particles Containing a Heavy Quark c or b.- Exercises.- 24 The Neutral Current and the Determination of sin2?w.- 24.1 Neutrino–Electron Scattering.- 24.2 Neutrino–Nucleon Scattering.- 24.3 Effects of the Weak Interaction in Electron–Positron Annihilation.- Exercises.- 25 The Physics of the Z-, W-, and Higgs Bosons.- 25.1 The Z-Boson.- 25.2 The W-Boson.- 25.3 The Production of W- and Z-Bosons in p$$
\bar p
$$ Collisions.- 25.4 The Spin of the W-Boson.- 25.5 The Higgs Boson.- Exercises.- 26 The System of Neutral K-Mesons and CP Violation.- 26.1 Phenomenology of the Neutral K-Mesons.- 26.2 CP Violation and CPT Invariance in the Standard Model.- 26.2.1 CP Violation in the Lagrange Density.- 26.2.2 CPT Invariance.- 26.2.3 CP Violation in the Neutral K-Meson System in the Standard Model.- Exercises.- 27 Order and Disorder in Elementary Particle Physics.- 27.1 Grand Unification.- 27.2 Further Symmetries at Intermediate Energies.- 27.3 Supersymmetry, Strings, and Superstrings.- 27.4 Order Out of Chaos.- Appendices A Dirac Matrices and Spinors.- B The Feynman Rules of QED.- C The Groups SU(2) and SU(3).- C.1 The Group SU(2).- C.2 The Group SU(3).- D The Feynman Rules of QCD.- F The Fierz Transformation.- G The Feynman Rules for the Standard Model in the Unitary Gauge.- H The Kobayashi–Maskawa Matrix for Three Families.- I.1 General Formalism.- I.2 Application to the System of Neutral K-Mesons.- J Solutions to Selected Exercises.- References.