Bachelor

** Quantenmechanik ** - * Details Hier *

Master

14756 | ** Quantum Field Theory II**

Primary Areas of Specialization: GR/QFT

Tutors:

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

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.