Winter Term 2026/27

14756.2008 | Quantum Field Theory I

Primary Areas of Specialization: GR/QFT
This course gives an introduction to quantum field theory from the viewpoint of condensed matter physics. The lecture series QFT I+II is strongly recommended to anyone interested in theoretical quantum physics. Knowledge of quantum mechanics is mandatory. While knowledge of the Advanced Quantum Mechanics course is useful, it is not required.

Lectures
Tuesday 08:00 - 09:30
Friday 12:00 - 13:30
The first lecture will be on October 13th. The lecture takes place in Seminar room 0.03, new theory building.

Tutorials
Wednesday 10:00 - 11:30 (Seminar room 0.01, new theory building)
Wednesday 12:00 - 13:30 (Seminar room 0.02, new theory building)

Contact
Foster Thompson (lead tutor) <fthompson@uni-koeln.de>
Orla Supple <osupple@uni-koeln.de>
Oleksandr Sulyma <osulyma@uni-koeln.de>
Rohan Mittal <rmittal1@smail.uni-koeln.de>
Rohit Kantipudi <rkantipu@smail.uni-koeln.de>

Contents
Classical field theory: action principle; continuum limit; functional calculus; symmetries and Noether theorem
Quantum field theory: Fock space and second quantization; representation of Fock space operators; applications: ultracold bosonic atoms; fermions and spins in one dimension
Path integral quantization I: Feynman path integral of single particle quantum mechanics; applications: semiclassical limit; tunneling problems and instantons; quantum vs. statistical physics
Path integral quantization II: Bosonic and fermionic many-body problem; quantum statistical partition function; correlation functions and time ordering; Matsubara formalism; application: boson-fermion duality in 1+1 dimension
Diagrammatic expansion and renormalization: Perturbation theory and Feynman diagrams; generating functionals and effective action; Dyson-Schwinger equations; resummation; large N expansion; application: resonant atom scattering

Literature
A. Altland, B. Simons, “Condensed Matter Field Theory”, Cambridge University Press (2010) – Broad compendium on both physics and techniques.
J. Negele, H. Orland, “Quantum Many-Particle Systems”, Advanced Books Classics (1998) – Functional integrals, many-body techniques.
A. Zee, “Quantum Field Theory in a Nutshell”, Princeton University Press (2010) – Gentle and conceptual introduction.
X.-G. Wen, “Quantum Field Theory of Many-Body Systems”, Oxford Graduate Texts – Another gentle and conceptual introduction with focus on gauge theories.
S. Sachdev, “Quantum Phase Transitions”, Cambridge University Press (2011) – Overview of paradigmatic quantum models and their physics.
M. Peskin, D. Schroeder, “An Introduction to Quantum Field Theory”, Frontiers in Physics (1995) – High energy perspective.