Non-linear supersymmetric Sigma-Model for Scalar Classical Waves

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.