- Aug.03: Our first class will be in MP1115 from 11:10am-12:00noon on Thursday 4th January 2017 (the first day of Winter/Spring semester). I will begin with organizational matters, and then start discussing the physics of Noether's Theorem. See you there!

I recommend QFT textbooks by Michael Peskin & Daniel Schroeder, Lewis Ryder, Pierre Ramond, Tom Banks, Steven Weinberg, Mark Srednicki, Ta-Pei Cheng and Ling-Fong Li, and Tony Zee.

I provide my own frequently updated lecture notes for free online. [expect a few typos!]

Assessment will be based on five equally weighted components: four homework assignments and a final exam. Homeworks will be due on Jan.29, Feb.19, Mar.12, and Apr.02. The final exam will be to compute the one-loop beta function of QCD together, and will involve both individual and group work, held over over two adjacent days.

- Symmetries and Conservation Laws
- Noether's Theorem, Continuous (Lie) Groups, The Lorentz Algebra, Casimir Operators and Lorentz Irreps, Abelian gauge symmetry and QED, Nonabelian gauge symmetry, Yang-Mills Lagrangian, Yang-Mills equations of motion, Yang-Mills vs General Relativity, Chirality and the Standard Model, Gauging isospin and hypercharge
- Spontaneous Symmetry Breaking
- Goldstone's Theorem and Spontaneous Symmetry Breaking (SSB), SSB with global symmetry: Linear Sigma Model, SSB with local gauge symmetry: Abelian Higgs, Summary for U(1) Goldstone and Higgs, SSB, Non-Abelian Gauge Symmetry, and the Standard Model, The Higgs boson, SSB: Higgsings and Vector Bosons, SSB: Higgsing and Fermion Masses
- The Feynman Path Integral
- FPI for non-relativistic point particles, Functional quantization for scalar fields, How to pick off correlation functions, Free massive scalar field, Functional determinants, Free two-point correlation function, Free four-point correlation function, General potentials
- Generating functionals and the Schwinger-Dyson equations
- The generating functional for all Feynman graphs, The generating functional for free scalar field theory, Analogy between Statistical Mechanics and QFT, The generating functional and the Schwinger-Dyson equations, Feynman rules for scalar field theory, Generating functional for connected graphs W[J], Semiclassically speaking, Quantum [effective] action and Legendre trees, The S-matrix and the LSZ reduction formula, Kaellen-Lehmann spectral representation for interacting QFTs
- Functional Quantization for Spin Half
- FPI Quantization for Fermions: Grassmann Variables, Grassmann Integration, Gaussians, Functional determinants, Dirac Fields, Generating Functional for Dirac Fermions, Fermionic Sources, Grassmann Derivatives, Weyl and Majorana fields
- Functional Quantization for Spin One
- U(1) Quantum Electrodynamics, Gauge Invariance, Fadeev-Popov Procedure: Abelian case, Gauge-Fixed Photon Action at Tree Level, Functional quantization for Yang-Mills fields: quick version, Fadeev-Popov ghosts for Yang-Mills fields, Lorentz gauge Feynman rules for Yang-Mills, BRST invariance and unitarity
- Renormalization and Quartic Scalar Field Theory
- Length Scales, Cutoffs, Focus: 1PI Diagrams in $\phi^4$, Divergences in $\phi^4$ in D=4, Divergences in General, Weinberg's Theorem, Dimensional Regularization and the Propagator Correction, Vertex Correction, Counterterms
- Callan-Symanzik equation and Wilsonian Renormalization Group
- Counterterms, Callan-Symanzik Equation, Fixed Points, Wilsonian RG and UV cutoffs
- One loop renormalization of QED
- Power counting, Photon self-energy a.k.a. Vacuum Polarization, Electron self-energy, QED Vertex Correction, Ward-Takahashi Identities in QED, Photon masslessness and Charge Renormalization, The Optical Theorem and Cutkosky Rules, Counterterms and the QED beta function
- An introduction to chiral anomalies
- Anomalies in Path Integral Quantization, Triangle anomaly: the Feynman Diagram approach, Anomaly cancellation for chiral gauge field theories