Quark loop in QCDDr. A. J. Tolley and Dr. C. de Rham

30 hours

Office hourTuesdays 3pm, room H506

 Part I: Path integral for scalar fields (C. de Rham)

Functional methods
Path integrals in quantum mechanics and QFT.
Perturbation theory and Feynman diagrams.
Feynman rules from path integrals.

Ultraviolet divergences and regularisation.
Renormalised perturbation theory. 
Wilsonian renormalisation.
Renormalisation group.
Callan-Symanzik equation.
Dimensional regularisation.

 Part II: Path integral for Fermions & Gauge Fields (Dr. A. J. Tolley)

Path integral for fermions
Fermions and Grassman variables

Non-Abelian gauge field theory
Abelian and non-Abelian gauge symmetries.
QCD and Yang-Mills theory.
Gauge fixing and Faddeev-Popov ghosts.
Computation of the beta function.
Asymptotic freedom, colour confinement and the continuum limit.

Course material

Lecture notes, problems and solutions can be found on Blackboard‌


  • Peskin & Schroeder, An Introduction to Quantum Field Theory, (Westview Press, 1995)
  • Srednicki, Quantum Field Theory, (Cambridge University Press, 2007)
    Another good general textbook, organised differently
  • Ryder, L., Quantum Field Theory, (Cambridge University Press, 2006)
    Very good for explicit derivations
  • Bailin & Love, Introduction to Gauge Field Theory, (IOP Publishing, 1993)
    Very good for practical calculations
  • Maggiore, M.,  A Modern Introduction to Quantum Field Theory, (Oxford University Press 2005)
    Very pedagogical
  • Das, A., Field Theory A path Integral Approach, 2nd edition, World Scientific Lecture Notes in Physics – Vol 75 (2006)
    Very good path intergal approach
  • Le Bellac, Quantum and Statistical Field Theory, (Oxford University Press, 1991
    Especially renormalisation
  • Weinberg, Quantum Theory of Fields I& II, (Cambridge University Press, 1995)
  • Zee, Quantum Field Theory in a Nutshell, (Princeton University Press, 2003)
    Good explanation of conceptual points