Department of Physics

Lecture

Master

14756 | Quantum Field Theory II
Montag 12:00 bis 13.30, Seminarraum 0.01 Neubau
Mittwoch 08.00 bis 9.30, Seminarraum 0.01 Neubau
Ausnahme Mittwoch 11.10.: Konferenzraum alte Theorie
Übung Donnerstag 12.00 bis 13.30 (Seminarraum 0.01 Neubau)

Primary Areas of Specialization: GR/QFT

Tutors:
Dr. Alessio Chiocchetta (achiocch [at] thp.uni-koeln [dot] de)
Dr. Steven Mathey (smathey [at] thp.uni-koeln [dot] de)

Lecture notes and exercises

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

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.

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.