Quantum Field Theory

• Functional (path integral) quantisation of bosonic and fermionic fields
• Green functions
• Perturbation expansion, Feynman diagrams
• Particle states, LSZ reduction and cross sections
• Gauge invariance and quantisation of non-abelian gauge theories
• Ward-Takahashi identities
• Loop calculations and UV regularisation
• Dimensional regularisation
• Renormalisation, in particular of gauge theories
• Next-to-leading order effects in gauge theories (e.g. anomalous
• magnetic moment, infrared divergences and soft bremsstrahlung)
• Effective field theory
• Renormalisation group, running couplings and masses

After successful completion of the module the student will be prepared

• to compute Green functions in perturbation theory, including loop corrections, and apply these to calculations of high-energy reactions;
• to quantise non-Abelian gauge theory and to calculate tree- and loop processes;
• to understand the concepts of regularisation and renormalisation and to apply these in calculations;
• to improve perturbative calculations using the renormalisation group;
• to construct effective quantum field theories.

The course is accompanied by homework problems.

Blackboard, possibly supplemented with slides.

• Peskin & Schroeder, "An Introduction to Quantum Field Theory"
• Itykson & Zuber, "Quantum Field Theory"
• Bailin & Love, "Introduction to Gauge Field Theories"

The learning outcome is tested in a written exam of 180 minutes duration. Participation in tutorials is strongly recommended.

There will be a bonus (one intermediate stepping of "0,3" to the better grade) on passed module exams (4,3 is not upgraded to 4,0). The bonus is applicable to the exam period directly following the lecture period (not to the exam repetition) and subject to the following conditions

1. The student prepared at least 50% of the exercises on the exercise sheets and
2. presented at least three exercises at the blackboard and
3. actively participated in the tutorials.