Introduction To Quantum Field Theory And The Standard Model

Description

Contents Preface 1. Special Relativity 1.1 Notations and Conventions 1.2 Lorentz Transformations 1.2.1 Examples of Lorentz tranformations 1.2.2 General 4-vector 1.2.3 Tensor 1.3 Mechanics 1.3.1 Covariant equation of motion 1.4 Lagrangian Formulation 1.4.1 Free particle 1.4.2 Particle in an electromagnetic field 1.5 Fields and Derivatives 1.5.1 Scalar field 1.5.2 Vector field 1.5.3 Tensor field 1.5.4 Partial derivatives 1.6 Electrodynamics 1.6.1 Potentials 1.6.2 Field strengths 1.6.3 Gauge transformations 1.6.4 Electromagnetic current 1.6.5 Maxwell’s equations 1.6.6 Energy-momentum tensor 2. Elements of Relativistic Quantum Field Theory 2.1 Klein–Gordon Equation 2.1.1 Relativistic quantum mechanics of spin-0 particles 2.1.2 Quantum field theoretical formulation 2.1.3 Current and charge 2.1.4 Mechanical observables 2.2 Dirac Equation 2.2.1 Relativistic quantum mechanics of spin-1/2 particles 2.2.1.1 Observables 2.2.1.2 Dirac matrices 2.2.1.3 Covariant version of the Dirac equation 2.2.1.4 Conserved current 2.2.2 Solutions of the Dirac equation 2.2.2.1 Solutions with e−ipx 2.2.2.2 Solutions with e+ipx 2.2.2.3 Normalization 2.2.2.4 Polarization sum 2.2.2.5 Physical interpretation of the solutions 2.2.3 Quantum field theoretical formulation 2.2.3.1 Current operator and charge 2.2.3.2 Mechanical observables 2.2.3.3 Charge conjugation 2.3 Lorentz Symmetry and Dirac Equation 2.3.1 Lorentz transformations and spinors 2.3.1.1 Rotation 2.3.1.2 Boost 2.3.1.3 Boost and rotation 2.3.1.4 Boost from the rest frame 2.3.2 Covariance of the Dirac equation 2.3.3 Lorentz covariants 2.4 Dirac Particle in an External Electromagnetic Field 2.4.1 Electrostatic Coulomb field 2.4.2 Static magnetic field 3. Quantum Electrodynamics 3.1 Free Electromagnetic Field 3.1.1 Quantized electromagnetic field 3.1.2 Mechanical observables 3.2 Interacting Electromagnetic Field 3.3 Interacting Dirac-Field 3.4 Interaction and Time Evolution 3.5 S-Matrix Elements and Feynman Graphs 3.5.1 Modus operandi for the calculation of matrix elements 3.5.2 Extension to all fermions 3.6 Cross Section 3.6.1 Special case: 2-particle processes 3.6.2 Unpolarized cross section 3.6.3 Decay width 3.7 On the Calculation of Cross Sections 3.7.1 Spinors in matrix elements 3.7.2 Traces over Dirac matrices 3.7.3 Polarization sum for photons 3.8 Precision Tests of QED 3.8.1 Precision tests at low energies 3.9 Addendum: Coulomb Gauge and Feynman Graphs 3.9.1 Classical solution for the radiation field 4. Lagrangians and Symmetries 4.1 Lagrangian Formalism for Fields 4.1.1 Scalar field 4.1.2 Dirac field 4.1.3 Vector field 4.2 Space–Time Symmetries 4.2.1 Translational invariance and 4-momentum 4.2.1.1 Scalar field 4.2.1.2 Dirac field 4.2.1.3 Electromagnetic radiation field 4.2.2 Rotational invariance and angular momentum 4.2.2.1 Scalar field 4.2.2.2 Dirac field 4.2.2.3 Electromagnetic radiation field 4.3 Gauge Symmetry and QED 4.3.1 Local gauge transformations 4.3.2 Summary 4.4 Non-Abelian Gauge Symmetries 4.4.1 Global gauge symmetry 4.4.1.1 Mathematical insertion: Representation 4.4.2 Local gauge symmetry 4.4.2.1 Amendment 4.4.3 Dynamics of the gauge fields 4.4.3.1 Gauge field propagators 4.4.4 Gauge fixing and ghost fields 4.4.4.1 BRST symmetry 4.4.5 Perturbation theory and Feynman graphs 5. Quantum Chromodynamics 5.1 Formulation of QCD 5.1.1 Feynman rules 5.2 QCD Processes at High Energies 5.2.1 Processes at hadron colliders 5.3 Running Coupling Constant 5.3.1 Fine structure constant of QED 5.3.2 Fine structure constant of QCD 5.4 Parton Distributions 5.4.1 Parton model 5.4.2 Deep-inelastic scattering 5.4.3 Parton distributions and QCD 5.5 Hadronic Bound States 5.5.1 Representations of SU(3) 5.5.2 Hadron states 6. Electroweak Theory 6.1 Historical Overview 6.2.1 Chirality 6.3 V–A Theory and Massive Vector Bosons 6.3.1 Formulation for leptons 6.3.2 Muon decay in the Fermi model 6.3.3 Intermediate vector bosons 6.3.4 Extension to quarks 6.3.5 Deficiencies of the V–A theory 6.4 Electroweak Standard Model 6.4.1 Symmetry group and global gauge invariance 6.4.2 Local gauge invariance 6.4.3 Dynamics of the gauge fields 6.4.4 Gauge-boson masses and Higgs mechanism 6.4.4.1 Abelian model 6.4.4.2 SU(2)×U(1) model 6.4.5 Fermion masses and Yukawa interaction 6.4.5.1 Leptons 6.4.5.2 Quarks 6.5 Phenomenology and Tests of the Standard Model 6.5.1 Neutral currents and neutrino scattering 6.5.1.1 Neutrino–electron scattering 6.5.1.2 Neutrino–nucleon scattering 6.5.2 The vector boson masses 6.5.2.1 Muon decay and the vector-boson mass correlation 6.5.3 Vector bosons in electron–positron annihilation 6.5.3.1 Z resonance 6.5.3.2 On-resonance asymmetries 6.5.3.3 W-boson pair production 6.5.4 Electroweak precision tests 6.5.4.1 The vector boson mass correlation 6.5.4.2 Z resonance observables 6.6 Higgs Bosons 6.6.1 Higgs boson production 6.6.2 Higgs boson decays 6.6.3 Experimental studies 6.7 Open Questions Bibliography Index