- Correlation functions of quantum fields.
- Lehmann–Symanzik–Zimmermann reduction formula.
- Dimensional Analysis and Renormalizability.
- QED Feynman rules in the counterterm perturbation theory.
- Renormalization of the EM field at one loop.
- Ward–Takahashi identities.
- Spontaneous symmetry breakdown.
- 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.
- Optical Theorem for Soft Photons.
- Gauge dependence of QED counterterms.
- Vacuum energy and effective potential.
- Higgs Mechanism.
- Renormalization scheme dependence and the Minimal Subtraction.
- Introduction to gauge theories.
- Path integrals in quantum mechanics.
- Path integral for the harmonic oscillator (in detail).
- Functional integration in quantum field theory.
- 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.
- QCD beta function.
- Non-linear sigma models.

- Aharonov-Bohm effect and magnetic monopoles.
- Notes on canonical quantization
- Fock space formalism.
- Operators in the Focks space and wave function languages..
- Expansion of relativistic fields into creation and annihilation operators.
- The saddle point method.
- Propagators and Green's functions.
- Dirac spinor fields.
- Grassmann numbers (Wikipedia article).
- Fluctuations in the superfluid and the Bogolyubov transform.
- Fermionic algebra and Fock space; particles and holes.
- Finite multiplets of the Lorentz group [solutions to the exercises].
- Relativistic causality and the Feynman propagator for the fermions.
- Spin-statistics theorem.
- 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.
- Wigner and Nambu–Goldstone modes of symmetries.
- QCD Feynman rules.
- The Higgs mechanism.
- Glashow–Weinberg–Salam theory of weak and EM interactions.
- Quarks and leptons in the Glashow–Weinberg–Salam theory.

*Lie Agebras in Particle Physics: from Isospin to Unified Theories*by Howard Georgi, 1999, Westview press, ISBN 9780813346113. (UT library ebook).*Group Theory for Unified Model Building*by Richard Slansky, Physics Reports 79 (1981) pp. 1-128. (local copy)*Monopoles, Instantons, and Confinement*by Gerard 't Hooft, 1999 lectures at Saalburg, arXiv:hep-th/0010225.

Last Modified: April 27, 2019. Vadim Kaplunovsky

vadim@physics.utexas.edu