The coherent wave in a random uniaxial anisotropic medium

The coherent (mean) wave in an unbounded medium, characterized by random fluctuations superimposed on a deterministic background, is studied. Both the random fluctuations and the deterministic background are assumed to be uniaxial anisotropic. The procedure for obtaining the mean field is presented and generally follows the usual development of Dyson´s equation (the diagrammatical representation of the integrodifferential equation for the mean field) except for modifications needed to treat the anisotropy. The use of these modifications allows the Feynman diagrammatical representation of Dyson´s equation to remain unaltered except for the mass operator containing additional terms. An example is used to illustrate the procedure required to obtain an effective dielectric constant and the plane-wave dispersion relationship.