- Why study QFT?
- Intro to classical field theory.
- Relativistic electromagnetic fields.
- Review of canonical quantization.
- Intro to quantum fields.
- Spectrum of the free scalar quantum field.
- Second quantization of bosons.
- Expansion of relativistic fields into creation and annihilation operators.
- The saddle point method.
- Relativistic causality.
- Propagators and Green's functions.
- Noether theorem.
- Local symmetries and gauge theories.
- Bose–Einstein condensate and superfluidity.
- Aharonov–Bohm effect and magnetic monopoles.
- Particle and field multiplets of Lorentz symmetry.
- Dirac spinor fields.
- Grassmann numbers (notes from CEA, France); see also Wikipedia article.
- Fermionic algebra and Fock space; particles and holes.
- Charge congugation, Majorana and Weyl fermions, parity and CP.
- Relativistic causality and Feynman propagator for the fermions.
- Perturbation theory, Dyson series, and Feynman diagrams.
- Phase space factors.
- Mandelstam's variables
*s*,*t*, and*u*. - Dimensional analysis and allowed couplings.
- EM quantization and QED Feynman rules.
- Dirac trace techniques and muon pair production.
- Crossing Symmetry.
- Ward Identities and sums over photon polarizations.
- Annihilation and Compton Scattering.
- Spontaneous symmetry breaking.
- The Higgs mechanism.
- Glashow–Weinberg–Salam theory of weak and EM interactions.
- Quarks and leptons in the Glashow–Weinberg–Salam theory.
- Kaons, CP violation, and CKM matrix (prof. Mark Thomson's lectures at Cambridge U, Fall 2009); local copy.
- Neutrino masses in the Standard Model.

- Basics of dimensional regularization.
- Optical Theorem.
- Resonances.
- Correlation functions of quantum fields.
- Lehmann–Symanzik–Zimmermann reduction formula.
- Dimensional Analysis and Renormalizability.
- QED: counterterms, Feynman rules, divergences, and renormalizability.
- Renormalization of the EM field at one loop.
- Ward–Takahashi identities:
- Vacuum energy and effective potential.
- Form factors.
- QED vertex correction: the algebra, the anomalous magnetic moment, the electric form factor, the infrared divergence, the observed cross-sections, and the Appendix.
- Gauge dependence of QED counterterms.
- Introduction to the renormalization group.
- Plot of the running QCD coupling.
- Renormalization scheme dependence and the Minimal Subtraction.
- Path integrals in quantum mechanics.
- Functional integration in quantum field theory.
- Euclidean spacetime, discretization, and QFT ↔ StatMech analogy.
- Functional quantuzation of fermion fields.
- Functional quantisation of the electromagnetism.
- Quantization of non-abelian gauge theories and the Faddeev–Popov ghosts.
- QCD Feynman rules and QCD Ward Identities.
- BRST symmetry.
- Renormalizability of non-abelian gauge theories.
- QCD beta function.
- Non-linear sigma models.

*Lie Agebras in Particle Physics: from Isospin to Unified Theories*by Howard Georgi, 1999, Westview press, ISBN 9780813346113. (UT library ebook) [first semester].*Monopoles, Instantons, and Confinement*by Gerard 't Hooft, 1999 lectures at Saalburg, arXiv:hep-th/0010225 [second semester].- Magnetic monopoles, Duality, and SUSY (1995 Trieste lectures by Jeffrey Harvey).

Last Modified: April 24, 2021. Vadim Kaplunovsky

vadim@physics.utexas.edu