Department of Physics



Quantenmechanik - Details Hier



14756 | Quantum Field Theory II
Primary Areas of Specialization: GR/QFT

Dr. Alessio Chiocchetta (achiocch [at] thp.uni-koeln [dot] de)

First week:
Wed Oct. 10, 08.00 - 09.30 ETP seminar room 0.01
Fri Oct. 12, 08.00 - 09.30. physics seminar room 223/224
From the second week on:
Mon 12.00 - 13.30 ETP seminar room 0.01
Wed 08.00 - 09.30 ETP seminar room 0.01
Tutorials (starting Oct. 11):
Thu 14.00 - 15.30 ETP seminar room 0.03

This course extends the introduction to quantum field theory from the viewpoint of condensed matter physics, focusing on collective phenomena.

Lecture notes and exercises

Topics include:
- 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; superconductors: Meissner effect and Anderson-Higgs mechanism; insulators: Hall conductivity and Chern-Simons action; 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.
- Topological phase transitions: classical XY model, electrostatic duality, vortex defects; Kosterlitz-Thouless transition via real space RG; relation to Sine-Gordon field theory; quantum XY model: electrodynamic duality and phase structure in various dimensions.

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.