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