Course data
Course name: Quantum Field Theory
Neptun ID: BMETE15MF65
Responsible teacher: Gábor Takács
Programme: Courses for Physicist MSc students
Course data sheet: BMETE15MF65
Requirements, Informations

Informations for semester 2022/23/2



The course consists of 3x45 minutes of lectures and an exercise class of length 2x45 minutes per week. The language of the course is English; consultation in Hungarian is available upon request.


Printed material for the lectures will be made available in Teams during the semester.


Lectures are on every Tuesday, 10:15-13:00 in room F3M01.

Exercise classes are on every Thursday, 09:15-11:00 in room F3M01.


Problem sheets and exercise classes

Problem sheet 1 (to be discussed on Mar 02) 

Problem sheet 2 (to be discussed on Mar 09) 

Problem sheet 3 (to be discussed on Mar 16) 

Problem sheet 4 (to be discussed on Mar 23) 

Problem sheet 5 (to be discussed on Mar 30) 

Problem sheet 6 (to be discussed on Apr 13)

Problem sheet 7 (to be discussed on Apr 20)

Problem sheet 8 (to be discussed on Apr 27)

Problem sheet 9 (to be discussed on May 04)

Problem sheet 10 (to be discussed on May 11)

Problem sheet 11 (to be discussed on May 18)

Problem sheet 12 (to be discussed on May 25)

Problem sheet 13 (to be discussed on June 01)


Students are expected to attempt to solve these problems before the next exercise class. The first problem set consists of background material on classical field theory not covered in, but necessary for the course. 


Starting from the second problem sheet, students are randomly assigned problems from the list, the solution of which they must present at the exercise class. Every time at most 5-6 students get an assignment, and everyone gets assigned a problem every 2 or 3 weeks depending on the number of students. At the end of the semester their performance will be evaluated on the basis of these presented solutions.


To obtain the course signature, students must fulfill the usual attendance requirements for the exercise classes, i.e. they cannot miss more than 30% of them (i.e. students can be absent at most 4 times), and must also complete reporting on all their problem assigments.  There is no formal attendance requirement for the lectures.


Exam and final evaluation

For the exam every student must select a project which is built around some longer computation or derivation that must be studied using the available literature. The students are expected to understand calculations and arguments in depth and fill in missing details.
The projects are available at
To choose a project, please write your name next to it (Column C).
The exam is oral and consists of a presentation of the project, and answering short questions about the lecture material.
The final evaluation is the result of combining the results of the exercise class and the exam.


Topics covered

  1. Canonical quantisation. Quantised Klein-Gordon and Dirac fields. Spin-statistics theorem.
  2. Interacting fields. CPT theorem. Scattering theory and the S-matrix. Unitarity and microcausality. 
  3. Perturbation theory, Feynman rules for correlation functions.
  4. Asymptotic states. Feynman rules for the S matrix. Cross sections and decay rates.
  5. Quantisation of the electromagnetic field. Gauge invariance.
  6. Kallen-Lehmann representation, sum rules. LSZ reduction formulae.
  7. Feynman path integral in Hamiltonian and Lagrangian formalism.
  8. Functional formalism. Generator functionals. Free fields, Wick theorem.
  9. Grassmann variables and path integrals for fermions. 
  10. Renormalisation theory. Classification of divergences, counter term formalism. 
  11. Symmetries and Ward identities. Spontaneous symmetry breaking.
  12. Renormalisation group, Callan-Symanzik equation. Connection with theory of critical phenomena.


Recommended reading


  • M.E. Peskin and D.V. Schroeder: An Introduction to Quantum Field Theory (1995, Addison-Wesley)
  • C. Itzykson and J-B. Zuber: Quantum Field Theory (2006, Dover Publications)
  • S. Weinberg: The Quantum Theory of Fields I-III (1995, 1996, 2000, Cambridge University Press)
  • Notes for cross sections and decay rates