Nonlinear Sigma Model for Normal and Superconducting Systems: A Pedestrian Approach

Abstract

The nonlinear sigma model (NLSM) epitomises a field-theoretical approach to (interacting) electrons in disordered media. These lectures are aimed at the audience who might have vaguely heard about its existence but know very little of what is that, even less so of why it should be used and next to nothing of how it can be applied. These what, why and mainly how are the subject of the present lectures. In the first part, after a short description of why to be bothered, the NLSM is derived from scratch in a relatively simple (but still rather mathematical) way for non-interacting electrons in the presence of disorder, and some illustration of its perturbative usage is given. In the second part it is generalised, not without some leap of faith, to include the Coulomb repulsion and superconducting pairing.