Quantum Field Theory
This is the mandatory Quantum Field Theory course of the Master in Theoretical Physics at the University of Wrocław. It is tailored towards master and PhD students who are familiar with
- quantum mechanics
- special relativity
- quantum electrodynamics.
There are many good books on the subject, two of the classics are
- Peskin, Schroeder: An introduction to quantum field theory
- Weinberg: The Quantum Theory of Fields, Volume 1 & 2.
We will follow mostly the first one in the lectures and resort to Weinberg for details. There will be 2 hours of lectures and 2 hours of tutorials each week. For more information, please refer to the syllabus (in Polish) or contact me directly.
Additional material for the individual lectures, including the exercises which we discuss in the tutorials, is given below:
Reminder of spin 0 and 1/2 fields
Reminder of spin 1 fields, symmetries
Dimensional analysis, regularisation (cutoff, dimensional, PV)
QED at one loop (self-energy, vacuum polarisation)
Renormalised perturbation theory of QED (1)
Renormalised perturbation theory of QED (2)
Superficial divergences and power counting, renormalisability (
-function, RG flow
Path integral in QM, generating functional
Path integral for scalars, interactions, Feynman rules
Path integral for fermions
Path integral for spin-1 bosons, ghost fields
BRST symmetry, physical Hilbert space
Non-Abelian gauge theory, Feynman rules, QCD at one loop
Lie Algebras and Groups
Lie algebras describe infinitesimal symmetries of physical systems. Therefore, together with their representation theory, they are extensively used in physics, most notably in quantum mechanics and particle physics. This course introduces semi-simple Lie algebras, their representation theory and the corresponding groups for physicists. As a major application, we discuss Grand Unified Theories
(GUT). Moreover, we show how modern computer algebra tools like LieART can significantly help in all required computations throughout the course.