Field Theory in Condensed Matter Physics

In this class I will show, by examples, how field theory can describe some important phenomena in condensed matter physics.

The transition from a discrete to a continuum description is illustrated with the one-dimensional Harmonic chain both in classical and quantum mechanics.

Spontaneous symmetry breaking is introduced with the phenomenon of superfluidity for a weakly interacting Bose gas.

This is followed with the study of classical non-linear-sigma models and how to treat then using renormalization-group methods.

The Kosterlitz-Thouless phase transition is also discussed in details.

The concept of screening is introduced through the Jellium model for electrons at the level of the random phase approximation. Superconductivity is described within the mean-field and random-phase approximations.

The Caldeira-Leggett model for dissipation, in the context of a Josephson junction, is used to illustrate the role played by instantons in quantum mechanics.

If time allows it, bosonization will be covered in (1+1) dimensional spacetime.