B. Elattari et al., NONLINEAR SUPERSYMMETRIC SIGMA-MODEL FOR SCALAR CLASSICAL WAVES, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 57(3), 1998, pp. 2733-2738
We derive a nonlinear supersymmetric a model for the transport of ligh
t (classical waves) through a disordered medium. We compare this model
with the well-established nonlinear a model for the transport of elec
trons (Schrodinger waves) and display similarities of and differences
between both cases. We show that for weak disorder both models are equ
ivalent (have the same effective Lagrangian). This effective Lagrangia
n correctly reproduces the (different) Ward identities for Schrodinger
waves and for classical waves.