| 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 Non-abelian Gauge Symmetry |
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| 2 |
Broken Gauge Symmetry Abelian Higgs Model and its Quantization Spectrum: Massive Gauge Boson, No Ghosts, No Physical Massless Particle |
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| 3 |
Confinement Illustration of the Phenomenon in a Simple Model (Multi-Chern-Simons Theory) |
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| 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 |
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| 5 |
Quark and Lepton Multiplet Structure Choice of SU(3) and SU(2) Representations and Hypercharges to Represent the Observed Quarks and Leptons |
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| 6 |
Renormalizability Indications of Renormalization Theory Dimensional Criterion for Induced Terms Classification of Allowed Terms in the Standard Model |
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| 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 |
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| 8 |
CKM Matrix Appearance of Weak Mixing Angles and Irremovable Phase Schematic Discussion of Phenomenology |
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| 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 |
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| 10 |
Running Couplings Computation of the RG Functions Asymptotic Freedom Physical Interpretation: Antiscreening from Spin Paramagnetism |
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| 11 |
Simplest Applications Infrared Safety Derivation of Jet Antenna Patterns Brief Overview of Perturbative QCD |
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| 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 |
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| 13 |
Unification Using SO(10) Group Theory of Spinor Representation Breaking Scheme Quark and Lepton Quantum Numbers |
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| 14 |
Unification of Couplings Normalization of Hypercharge Computation of Effective Couplings Comparison with Observation |
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| 15 |
Lepton and Baryon Number Violation Low-dimension Operators for L and B Violation Microscopic Mechanisms Parameterization of Neutrino Mass Matrix |
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| Close-Up on the Higgs Sector | ||
| 16 |
Coupling to Matter Tree Graph Couplings Gluon Coupling through Heavy Quark Loops |
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| 17 |
Production and Decay Modes Associated Production with Gauge Bosons Gluon Fusion Computation of Decay Rates |
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| 18 |
Phenomenology of One and Two Doublet Models Two Doublet Models Practical Considerations on Signatures |
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| Anomaly Basics | ||
| 19 |
Examples of Anomalies Explicit Calculations in Simple Models Impossibility of Removal by Subtraction |
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| 20 |
Anomaly Cancellation Indications on Non-renormalization Theorem Application to Standard Model and Unified Models |
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| 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 |
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| 22 |
Nambu-Goldstone Bosons: Masses and Couplings Spontaneous Breaking of Approximate Chiral Symmetry Nambu-Goldstone Bosons Mass Formula Goldberger-Treiman Relation |
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| 23 |
The U(1)A Problem Absence of NG Boson for Axial Baryon Number Difficulty this Presents |
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| Instantons and U(1)A Breaking | ||
| 24 |
Topological Sectors in Gauge Theory Large Gauge Transformations θ Vacuum Lagrangian Interpretation |
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| 25 |
Interpolation with Instantons Semiclassical Passage between Sectors Action Bound Concrete Solution of the Euclidean Field Equations |
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| 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 |
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| Nonperturbative (Lattice) Formulation of Gauge Theory | ||
| 27 |
Formulation of the Gauge Sector Parallel Transporter Plaquette Action Dimensional Transmutation! |
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| 28 |
Strong Coupling and Confinement Color Sources and Wilson Criterion Strong Coupling Expansion |
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| 29 |
Formulation of the Fermions Straightforward Formulation and its Problems with Doubling Heavy Fermion Potential Domain Wall Fermions Link Fermions |
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