Quantum Field Theory (II)

Supplementary Notes

Class of Dr. Kaplunovsky, Spring 2019

Notes used (or expected to be used) in class

• 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.

Notes used for my QFT (I) class back in 2016

• Aharonov-Bohm effect and magnetic monopoles.
• Notes on canonical quantization
  • Poisson brackets and commutator brackets.
  • Heisenberg equations for quantum fields.
• 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.

Recommended Reading

• 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.