Non-linear supersymmetric Sigma-Model for Scalar Classical Waves

TL;DR

This paper derives a non-linear supersymmetric sigma-model for classical light waves in disordered media, compares it with the electronic wave model, and shows their equivalence under weak disorder conditions.

Contribution

It introduces a novel sigma-model for classical waves and analyzes its relation to the electronic wave model, highlighting similarities and differences.

Findings

Models are equivalent for weak disorder

Effective Lagrangian reproduces Ward identities

Differences in models for classical and electronic waves

Abstract

We derive a non-linear supersymmetric sigma-model for the transport of light (classical waves) through a disordered medium. We compare this model with the well-established non-linear sigma-model for the transport of electrons (Schroedinger waves) and display similarities of and differences between both cases. We show that for weak disorder, both models are equivalent (have the same effective Lagrangean). This effective Lagrangean correctly reproduces the (different) Ward identities for Schroedinger waves and for classical waves.