FC210 Advanced Quantum Field Theory

Faculty of Science
Spring 2026
Extent and Intensity
3/0/0. 4 credit(s). Type of Completion: z (credit).
In-person direct teaching
Teacher(s)
doc. Klaus Bering Larsen, Ph.D. (lecturer)
prof. Rikard von Unge, Ph.D. (lecturer)
Guaranteed by
prof. Rikard von Unge, Ph.D.
Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Contact Person: prof. Rikard von Unge, Ph.D.
Supplier department: Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Prerequisites
Passing of previous basic courses on classical and quantum statistical physics and thermodynamics.
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives
This course offers a comprehensive introduction into the methods and ideas of modern quantum field theory. The basic tool used is the path integral, which is introduced in detail and discussed thoroughly. The emphasis of the course is on explicit calculations, which are carried out in detail. At the end of the course the student is able to grasp the formalism of the path integral, the concept of renormalization, effective field theory, instantons, etc.
Learning outcomes
After finishing this course the student will: - understand the path integral as the basic calculational tool in QFT - perform basic calculations of correlation functions for scattering amplitudes - understand the uses renormalization - be familiar with the concept of effective field theory - be able to calculate also with fermions - understand the role of symmetry in path integrals - be an expert on the path integral treatment of gauge theories - understand gauge-fixing, ghosts and the role of BRST symmetry - be familiar with background field quantization - have experience with exact solutions and non-perturbative phenomenon of Yang-Mills theory
Syllabus
1. Path integral for free and interacting fields, perturbation theory, diagrammatic techniques, correlation functions, scattering amplitudes 2. Loop corrections for propagators and vertices, effective action, renormalization 3. Explicit calculations for scalar field, dimensional renormalization 4. Renormalization group, effective field theory 5. Spinors, Grassman variables, path integrals for fermions 6. Explicit calculations for fermions 7. Global and local symmetries, gauge invariance, gauge fixing, ghosts, BRST 8. Explicit calculations in non-abelian gauge theories 9. The method of background fields 10. Solitons, monopoles, instantons, Wilson loops
Literature
    recommended literature
  • SCHWARTZ, Matthew Dean. Quantum field theory and the standard model. 1st pub. Cambridge: Cambridge University Press, 2014, xviii, 850. ISBN 9781107034730. info
  • ZEE, A. Quantum field theory in a nutshell. 2nd ed. Princeton, N.J.: Princeton University Press, 2010, xvi, 576. ISBN 9780691140346. info
  • SREDNICKI, Mark Allen. Quantum field theory. 1st pub. Cambridge: Cambridge University Press, 2007, xxi, 641. ISBN 9780521864497. info
  • PESKIN, Michael Edward and Daniel V. SCHROEDER. An introduction to quantum field theory. Cambridge, Mass.: Perseus books, 1995, xxii, 842. ISBN 0201503972. info
  • ITZYKSON, Claude and Jean-Bernard ZUBER. Kvantovaja teorija polja : v 2-ch tomach. Translated by R. M. Mir-Kasimov. Moskva: Mir, 1984, 448 s. info
Teaching methods
Lectures, exercises
Assessment methods
Handed in solved problem sets and oral exam
Language of instruction
English
Further comments (probably available only in Czech)
The course is taught once in two years.
The course is taught every week.
General note: L.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2007, Spring 2008, Spring 2010, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2016, Spring 2017, Autumn 2019, autumn 2021, Autumn 2023, Spring 2024, Autumn 2025.
  • Enrolment Statistics (Spring 2026, recent)
  • Permalink: https://is.muni.cz/course/sci/spring2026/FC210