Updated Feb 25, 2019.

Quantum Field Theory (FK8027)

The course schedule can be found here .

Course Information for 2018/2019


  • The fourth homework set is available below. The submission deadline is Tuesday, March 05, 2019.

Text Book

Course Book: "Quantum Field Theory" by F. Mandl and G. Shaw (Second Edition from 2010) + lecture notes (

Supplementary reading:

  • "Classical Mechanics" by H. Goldstein, C. P. Poole, J. L. Safko (Chapter 13 for classical field theory and Noether's theorem)
  • "Quantum Field Theory and the Standard Model" by Matthew D. Schwartz (Cambridge University Press)
  • "Quantum Field Theory for the Gifted Amateur" by Tom Lancaster and Stephen Blundell (Oxford University Press)
  • "Quantum Field Theory in a Nutshell" by A. Zee (Princeton University Press)
  • Another book for path integrals in QFT is "Field Theory: A Modern Primer" by Pierre Ramond, (section 3.1, 3.2, 4.1 for path integrals).
  • "Gauge Theory of Elementary Particle Physics" by Ta-Pei Cheng and Ling-Fong Li (for Faddeev-Popov quantization)
  • "Quantum Field Theory" by Mark Srednicki (You can try a prepublication draft of this book on the author's webpage here


Detailed information about tutorial sessions can be found here .

Some Lecture Notes

These notes are meant to supplement the book.

Homework Problems

Problem set 1 (due date: Dec 7, 2018)
Problem set 2 (due date: Jan 08, 2019)
Problem set 3 (due date: Feb 15, 2019)
Problem set 4 (due date: March 05, 2019)

Grading Criteria

The course has 15 credits, 10 associated to homeworks and 5 to the final examination. Correspondingly, homeworks will contribute 65 % and the examination will contribute 35 % of the final grade. Adding the two, students will get a mark between 0 and 100. The A-F grade assignments are done as follows:

A (100-90), B (89-80), C (79-70), D (69-60), E (59-50), Fx (49-45), F (44-0).

To pass the course, both parts need to be completed.

Course Content

Examples of classical fields and field equations. Review of analytical mechanics of particles, Poisson brackets and quantization. Lagrangian and Hamiltonian formulations of classical field theory, the Euler-Lagrange equation. Lorentz transformations and SO(1,3), classical theories of scalar, vector and spinor fields.

Symmetries and conservation laws in field theory (proof and applications of Noether's theorem). Spacetime and global gauge symmetries. The energy-momentum tensor, conservation of charge, energy, momentum, angular momentum and spin.

Quantization of relativistic free fields: Real and complex scalar fields, conserved quantities, particle interpretation. The electromagnetic field, guage invariance and gauge fixing, the Gupta-Bleuler quantization, massive vector fields. The Dirac field, spinors as SO(1,3) representations, conserved quantities. Normal ordering. Covariant Commutation relations, Causality and the spin-statistics relation. Time ordering, The Feynman propagator and its contour integral representation for scalar, spinor and vector fields. The longitudinal and scalar photon contributions.

Interacting fields in QFT: Interactions from local gauge invariance (the Abelian case), electrodynamics. The interaction picture, the S-matrix and its expansion in perturbation theory, Wick's theorem.

Quantum Electrodynamics (QED): The S-matrix expansion of interactions in QED, basic processes to second order. Feynman diagrams, Feynman rules and the Feynman amplitude. The scattering cross-section, sum over spins and polarizations. Calculation of cross sections in Bhabha, Möller and Compton scatterings, etc. The basic ideas of loops and ultraviolet divergences, renormalization and running couplings .

Non-Abelian gauge theories (with a review of basic group theory, and Lie algebras, SU(n) groups). The basics of Quantum Chromodynamics (QCD) as the theory of strong interactions.

Introduction to (leptonic) Weak interactions, chiral fermions, massive vector fields, the V-A structure. Weak interactions as an SU(2)xU(1) gauge theory, identification of electromagnetism. Spontaneous symmetry breaking, Goldstone and Higgs mechanisms. Higgs mechanism in SU(2)xU(1) gauge theory, Yukawa couplings and fermion masses. The mass matrix and neutrino mixings. Theory of electroweak interactions and the standrd model of particle physics.

Path integral formulation of quantum field theory. Functional integrals for bosonic and fermionic fields. Interactions in the PI formulation. The generating function and perturbative expansions. Path integral quantization of Abelian and non-Abelian gauge theories, gauge fixing the and Faddeev-Popov procedure, the Faddeev-Popov ghosts.

Extra topics not always covered: Radiative corrections, regularization, renormalization, calculation of Lamb-shift and anomalous magnetic moment. Infrared divergences.

Expected Learning Outcomes

Upon completion of the course, students are expected to be able to:

  • Apply the relation between symmetries and conservation laws in field theory to compute energy, momentum, spin and charges for various types of fields;

  • Provide a mathematical treatment of the quantization of non-interacting scalar, Maxwell, and Dirac fields in the operator formalism, and give an account of the relation between quantized fields and elementary particles;

  • Give a mathematical treatment of interacting fields, and of the logical links between S-matrix elements, perturbation theory, Feynman diagrams and rules, scattering amplitudes and cross-sections, and be able to compute tree-level cross-sections for some basic scattering processes in Quantum Electrodynamics;

  • Give a mathematical account of non-Abelian gauge theories, and of the Electroweak theory and Higgs mechanism for leptons, and to compute tree-level cross-sections for some basic electroweak processes;

  • Provide a mathematical treatment of the path integral formulation of quantum field theory for interacting bosonic and fermionic fields by using the generating function method, including the Fadeev-Popov method for non-Abelian gauge theories.