Informal course on
Topological terms in condensed matter physics
Spring 2007, EPFL, Lausanne, Switzerland

Lecture 1: May 21, Monday, room PH31 (EPFL) 11h15 - 13h00.
Lecture 2: May 30, Wednesday, room PH31 (EPFL) 11h15 - 13h00.
Lecture 3: June 4, Monday, room PH33 (EPFL) 15h15-17h00
Lecture 4: June 11, Monday, room PH33 (EPFL) 15h15-17h00
Instructor: Dr. Alexander (Sasha) Abanov, Associate Professor
Office: PH H2 487
Phone: 3-5856
Web page:


The methods of quantum field theory are widely used in condensed matter physics. In particular, the concept of an effective action was proven useful when studying low temperature and long distance behavior of condensed matter systems. Often the degrees of freedom which appear due to spontaneous symmetry breaking or an emergent gauge symmetry, have non-trivial topology. In those cases the terms in the effective action describing low energy degrees of freedom can be metric independent (topological). I will try to give a simple classification of possible topological terms as well as some of their consequences. We will also discuss the origin of these terms and calculate effective actions for several fermionic models. In this approach topological terms appear as phases of fermionic determinants and represent quantum anomalies of fermionic models. In addition to the wide use of topological terms in high energy physics, they appeared to be useful in studies of charge and spin density waves, Quantum Hall Effect, spin chains, frustrated magnets, and some models of high temperature superconductivity.

Topics to be touched


Recommended Books

Geometry and topology

Quantum field theory in condensed matter physics

Topology in physics

Some of the homotopy groups used in physics (PDF )

Syllabus of the course

Last updated June 11, 2007