| Basic Concepts Underlying the Standard Model |
| 1 | Gauge Symmetry
Review of Gauge Symmetry in Electrodynamics, from both Point Particle and Field Perspectives
Coulomb Law and Physical Photons from the Propagator
Gauge Symmetry Required to Avoid Ghosts
Definition of Non-abelian Gauge Symmetry |
| 2 | Broken Gauge Symmetry
Abelian Higgs Model and its Quantization
Spectrum: Massive Gauge Boson, No Ghosts, No Physical Massless Particle |
| 3 | Confinement
Illustration of the Phenomenon in a Simple Model (Multi-Chern-Simons Theory) |
| Specific Structure of the Standard Model |
| 4 | Gauge and Higgs Sector
Lagrangian Model for SU(2)×U(1) Gauge-Higgs Sector
Mixing (Weinberg) Angle, Physical Spectrum and Coupling of the Gauge Bosons |
| 5 | Quark and Lepton Multiplet Structure
Choice of SU(3) and SU(2) Representations and Hypercharges to Represent the Observed Quarks and Leptons |
| 6 | Renormalizability
Indications of Renormalization Theory
Dimensional Criterion for Induced Terms
Classification of Allowed Terms in the Standard Model |
| 7 | Canonical Forms
Use of Field Re-definitions to Simplify the Allowed Terms
Accidental Symmetries of the Simplified Forms, both for QED/QCD and for the full Standard Model |
| 8 | CKM Matrix
Appearance of Weak Mixing Angles and Irremovable Phase
Schematic Discussion of Phenomenology |
| Renormalization Group and Asymptotic Freedom |
| 9 | Equations of the Renormalization Group
Couplings must be Normalized a Scale Point, but the Scale is Arbitrary
Different Choices related by Renormalization Group
Alternative Perspective (Wilson), "Integrating Out" High Momentum Modes |
| 10 | Running Couplings
Computation of the RG Functions
Asymptotic Freedom
Physical Interpretation: Antiscreening from Spin Paramagnetism |
| 11 | Simplest Applications
Infrared Safety
Derivation of Jet Antenna Patterns
Brief Overview of Perturbative QCD |
| Unified Gauge Theories |
| 12 | Unification of Quantum Numbers: SU(5)
Simple Breaking Scheme for SU(5) → SU(3)×SU(2)×U(1)
Identification of Hypercharge |
| 13 | Unification Using SO(10)
Group Theory of Spinor Representation
Breaking Scheme
Quark and Lepton Quantum Numbers |
| 14 | Unification of Couplings
Normalization of Hypercharge
Computation of Effective Couplings
Comparison with Observation |
| 15 | Lepton and Baryon Number Violation
Low-dimension Operators for L and B Violation
Microscopic Mechanisms
Parameterization of Neutrino Mass Matrix |
| Close-Up on the Higgs Sector |
| 16 | Coupling to Matter
Tree Graph Couplings
Gluon Coupling through Heavy Quark Loops |
| 17 | Production and Decay Modes
Associated Production with Gauge Bosons
Gluon Fusion
Computation of Decay Rates |
| 18 | Phenomenology of One and Two Doublet Models
Two Doublet Models
Practical Considerations on Signatures |
| Anomaly Basics |
| 19 | Examples of Anomalies
Explicit Calculations in Simple Models
Impossibility of Removal by Subtraction |
| 20 | Anomaly Cancellation
Indications on Non-renormalization Theorem
Application to Standard Model and Unified Models |
| Chiral Symmetry and the U(1)A Problem |
| 21 | Approximate Chiral Symmetry
'Unexpectedly' Small Masses of Pions
Enhanced Symmetry of QCD with Zero Quark Masses, Not Manifested in the Spectrum |
| 22 | Nambu-Goldstone Bosons: Masses and Couplings
Spontaneous Breaking of Approximate Chiral Symmetry
Nambu-Goldstone Bosons
Mass Formula
Goldberger-Treiman Relation |
| 23 | The U(1)A Problem
Absence of NG Boson for Axial Baryon Number
Difficulty this Presents |
| Instantons and U(1)A Breaking |
| 24 | Topological Sectors in Gauge Theory
Large Gauge Transformations
θ Vacuum
Lagrangian Interpretation |
| 25 | Interpolation with Instantons
Semiclassical Passage between Sectors
Action Bound
Concrete Solution of the Euclidean Field Equations |
| 26 | Functional Determinant and Fermion Zero Modes
Formal Evaluation of the Functional Integral
Collective Coordinates and Measure
Fermion Zero Modes and their Saturation
Fulfillment of Anomaly Equation |
| Nonperturbative (Lattice) Formulation of Gauge Theory |
| 27 | Formulation of the Gauge Sector
Parallel Transporter
Plaquette Action
Dimensional Transmutation! |
| 28 | Strong Coupling and Confinement
Color Sources and Wilson Criterion
Strong Coupling Expansion |
| 29 | Formulation of the Fermions
Straightforward Formulation and its Problems with Doubling
Heavy Fermion Potential
Domain Wall Fermions
Link Fermions |