Non – linear supersymmetric σ – Model for Scalar Classical Waves

We derive a non–linear supersymmetric σ–model for the transport of light (classical waves) through a disordered medium. We compare this model with the well–established non–linear σ–model for the transport of electrons (Schrödinger 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 Schrödinger waves and for classical waves.