Quantum field theory

Faculteit Science and Engineering
Jaar 2021/22
Vakcode WMPH018-05
Vaknaam Quantum field theory
Niveau(s) master
Voertaal Engels
Periode semester I b
Rooster rooster.rug.nl

Uitgebreide vaknaam Quantum field theory
Leerdoelen At the end of the course, the student is able to:
1. Derive the Feynman rules from a given Lagrangian and calculate cross sections and decay rates in scalar field theories, Yukawa theories and QED at the tree level of the quantised theory.
2. Recognise and explain the symmetry properties of the theories listed in objective 1 and derive the corresponding transformations of the fields and currents.
3. Derive the perturbative expansion of the path integral for the theories in objective 1 and derive the corresponding n-point correlation functions.
4. Classify the operators that contribute to quantum field theories with scalar, vector and spin 1/2 fermion fields in relevant, marginal and irrelevant and determine if the theory is super-renormalisable, renormalisable, or non-renormalisable.
5. Have a basic understanding of renormalisation and renormalised perturbation theory.
Omschrijving This course is devoted to the fascinating subject of field theories and their quantisation through a path integral description. This offers the best way to explore many quantum phenomena both in particle physics and statistical physics, and emphasis is given to their connection.

We start with the derivation of the path integral, from quantum mechanics to quantum field theory, and an analysis of its physical properties. In order of increasing complexity we then quantise theories containing scalar, vector and spin 1/2 fermion fields, derive the Feynman rules for these theories and compute cross sections and decay rates for processes at the tree level of the quantised theory.

The last part of the course is devoted to Quantum Electrodynamics (QED), an Abelian gauge theory, and we derive the Faddeev Popov quantisation in this case as a pedagogical example that anticipates the non-Abelian case. We also introduce the basics of renormalisation, specifically the dimensional analysis of Lagrangian operators and their classification in super-renormalisable, renormalisable and non-renormalisable. We explain renormalised perturbation theory for QED, but explicit one-loop calculations are left for later on (Elementary Particles, Master).
Uren per week
Onderwijsvorm Hoorcollege (LC), Opdracht (ASM), Werkcollege (T)
(32 LC, 16 T, 20 ASM, 72 self study)
Toetsvorm Schriftelijk tentamen (WE)
(WE 100%)
Vaksoort master
Coördinator prof. dr. E. Pallante
Docent(en) M.R. Boers, MSc. ,prof. dr. E. Pallante
Verplichte literatuur
Titel Auteur ISBN Prijs
Quantum field theory in a nutshell Zee, A. 0-691-01019-6
An introduction to quantum field theory Peskin, M.E. & D.V. Schroeder 0201503972
Entreevoorwaarden Quantum mechanics, Relativistic Quantum Mechanics
Opmerkingen The exam consists of three to four problems. The last problem is always devoted to objective 1. The first two to three problems probe objectives 2, 3, 4.

This course was registered last year with course code NAQVT-08
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