LEC #  TOPICS  

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 Nonabelian 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 (MultiChernSimons Theory) 

Specific Structure of the Standard Model  
4  Gauge and Higgs Sector Lagrangian Model for SU(2)×U(1) GaugeHiggs 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 Redefinitions 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 Lowdimension Operators for L and B Violation Microscopic Mechanisms Parameterization of Neutrino Mass Matrix 

CloseUp 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 Nonrenormalization 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  NambuGoldstone Bosons: Masses and Couplings Spontaneous Breaking of Approximate Chiral Symmetry NambuGoldstone Bosons Mass Formula GoldbergerTreiman 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 