Quark loop in QCDProf. Andrew J. Tolley 

30 hours

Office hourTBD, room H607

 Path integral for scalar fields 

Functional methods
Path integrals in quantum mechanics and QFT.

Generating Functions and Effective Action.

Feynman rules from path integrals.

Fermions and Grassman variables.

One-loop effective actions.

Ultraviolet divergences and regularisation.

Wilsonian renormalisation, Effective Actions.

Renormalisation group.

Callan-Symanzik equation.

Dimensional regularisation.

Non-Abelian gauge field theory

Abelian and non-Abelian gauge symmetries.

QCD and Yang-Mills theory.

Gauge fixing and Faddeev-Popov ghosts.

BRST/BV/Master Equation.

Computation of the beta function.


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