Relativistic Quantum Field Theory III

Calendar

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
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)AProblem 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