  We develop a framework for the multiple scattering of a polarized wave. We
consider particles with spin propagating in a medium filled with scatterers. We
write the amplitudes of each spin eigenstate in a local, mobile frame. One of
the axes is in the direction of propagation of the particle. We use this
representation to define a directional Green's operator of the homogeneous
medium and also to write the spin-dependent scattering amplitudes. We show that
this representation reveals a Berry phase. We establish a generalized
Green-Dyson equation for the multiple scattering problem in this framework. We
show that the generalized Green-Dyson equation can be solved by linear algebra
if one uses a representation of the rotations based on Wigner D-matrices. The
properties of light scattering are retrieved if we use spin 1 particles. Our
theory allows to take into account several kinds of anisotropies like circular
or linear dichroism and birefringence, Faraday effects andMie scattering within
the same formalism. Several anisotropies can be present at the same time.
