Path-integral quantum cosmology. II. Bianchi type I with volume-dependent source

The Feynman path-integral formalism is applied to the degrees of freedom of the fluid-filled Kasner (and related) cosmological models. The measure constructed for the vacuum analysis is used to effect the Arnowitt-Deser-Misner reduction to dynamical degrees of freedom within the functional integral. The Hankel transform of the minisuperspace transition amplitude is obtained. A perturbation expansion about the classical vacuum solution is presented.