Summer Term 2025
14756.2009 | Quantum Field Theory II
Primary Areas of Specialization: GR/QFT
This course extends the introduction to quantum field theory from the viewpoint of condensed matter physics, focusing on collective phenomena. he lecture series QFT I+II is strongly recommended to anyone interested in theoretical physics. Knowledge of quantum mechanics is mandatory. While knowledge of the Advanced Quantum Mechanics course is useful, it is not required.
The exam mode for this lecture is oral. The number of credit points is 9.
Lectures
Tuesday 10:00 - 11:30 - Seminarraum theorie 215
Wednesday 08:00 - 09:30 - Seminarraum theorie 215
The first lecture will be on April 8th.
There is a Slack workspace to discuss among students and with the lecturer/tutors, and get the most recent version of the lecture notes.
Registration link.
Tutorials
Friday 14:00 - 15:30 - ETP 0.02
Friday 16:00 - 17:30 - ETP 0.01
Contact (head tutors):
Dr. Romain Daviet (rdaviet [at] uni-koeln [dot] de)
Dr. Johannes Lang (jlang [at] thp.uni-koeln [dot] de)
Contact (tutors):
Rohan Mittal (rmittal [at] thp.uni-koeln [dot] de)
Orla Supple (osupple [at]uni-koeln [dot] de)
Contents
Quantum condensation and spontaneous symmetry breaking: weakly interacting bosons, condensation vs. superfluidity vs. off-diagonal order, Goldstone and Mermin-Wagner theorems; weakly interacting fermions and BCS mechanism, BCS-BEC Crossover, Hubbard-Stratonovich transformation; quantum phase transition and functional integral for the Bose-Hubbard lattice model.
Gauge theories:
real-time linear response to electromagnetic fields; geometry of gauge invariance; response of superconductors: Meissner effect and Anderson-Higgs mechanism; response of insulators: Hall conductivity and Chern-Simons action; anomalies; Ising lattice gauge theories and Elitzur's theorem; functional integral quantization of gauge theories.
Renormalization group:
universality and scaling hypothesis; RG transformations in real and momentum space; Wilson-Fisher Fixed point, epsilon expansion; functional RG.
Selected applications:
topological phase transitions: classical XY model, electrostatic duality, vortex defects; Kosterlitz-Thouless transition via real space RG; relation to Sine-Gordon field theory, electrodynamic duality; O(N) non-linear Sigma models.
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. Schoeder, “An Introduction to Quantum Field Theory”, Frontiers in Physics (1995) – High energy perspective.
Exercises
A sheet will be uploaded every Thursday, and be discussed the week after on Friday. You can hand in solutions to the tutors until Thursday the week of the tutorial. They will correct your sheet and give feedback.
