  A family of random models for bosonic quasi-particle excitations, e.g. the
vibrations of a disordered solid, is introduced. The generator of the
linearized phase space dynamics of these models is the sum of a deterministic
and a random part. The former may describe any model of N identical phonon
bands, while the latter is a d-dimensional generalization of the random matrix
model of Lueck, Sommers, and Zirnbauer (LSZ). The models are constructed so as
to exclude the unphysical occurrence of runaway solutions. By using the
Efetov-Wegner supersymmetry method in combination with the new technique of
superbosonization, the disordered boson model is cast in the form of a
supermatrix field theory. A self-consistent approximation of mean-field type
arises from treating the field theory as a variational problem. The resulting
scheme, referred to as a coherent potential approximation, becomes exact for
large values of N. In the random-matrix limit, agreement with the results of
LSZ is found. The self-consistency equation for the full d-dimensional problem
is solved numerically.
