Self-consistent Green's function formalism for acoustic and light scattering. Part 3: Unitarity and symmetry

This paper completes two previous papers in which we have developed the self-consistent Green's function formalism for acoustic and light scattering. It is concerned with the unitarity and symmetry properties of the interaction and far field scattering operator of this formalism. We will show that these are primarily mathematical properties, and that the principles of energy conservation and reciprocity, which express our physical experience, can be modeled by these mathematical properties. For this we have to distinguish two experimental configurations, and only one of these configurations will allow us to relate energy conservation to unitarity. Closely related to this are questions concerning the definition and measurability of the scattering quantities and the importance of the optical and generalized optical theorem. These questions will be also discussed from the point of view of the self-consistent Green's function formalism.