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

A general framework for multiple scattering of polarized waves including anisotropies and Berry phase