Prerequisites: fundamentals of classical mechanics, electrodynamics, special relativity and quantum mechanics
Motivation: it is an unsolved problem how to consistently merge general relativity with quantum physics. For special relativity there is an answer: relativistic quantum field theory (QFT). We attempt a pedagogical introduction to the methods and difficulties of this programme.
The course is based on L.Edelhäuser und A. Knochel, "Tutorium Quantenfeldtheorie"
(Springer 2016). This is a good text, though written in German. We give a synopsis of the part discussed and extend where appropriate; the lecture notes will appear on Moodle in English language. For further reading I recommend the following two of the many excellent texts on QFT:
M. Peskin und D. Schroeder, "Quantum Field Theory", Levant Books (2005)
L. Ryder, "Quantum Field Theory", CUP (1996)
The starting point of our discussion is the Klein-Gordon-equation for the scalar field (spin 0) on the example of which virtually all concepts of quantum field theory can be explained without complicating the matter by cluttering it with extra difficulties like spin or gauge symmetries. We will encounter
- canonical quantisation, propagators,
- interactions, the path integral formalism, Feynman graphs,
- scattering amplitudes and cross sections,
- regularisation and the basic features of renormalisation.
In the second half of the course (certainly in the new year) spin 1/2 and spin 1 fields will be introduced. We will discuss simple processes in quantum electrodynamics.