  Utilizing a number of results of Dittmann, we investigate the nature of the
Yang-Mills field over the eight-dimensional convex set, endowed with the Bures
metric, of three-level quantum systems. Parallelling the decomposition of
eight-dimensional Euclidean fields by Corrigan, Devchand, Fairlie and Nuyts, as
well as Figueoroa-O'Farrill and others, we investigate the properties of
self-dual and anti-self-dual four-forms corresponding specifically to our
Bures/non-Euclidean context. For any of a number of (nondegenerate) 3 x 3
density matrices, we are able to solve the eigenequation of the associated
Hodge * operator with respect to the Bures metric. We obtain sets of
(traceless) twenty-eight real eigenvalues, consisting of four singlets and
three octets. The associated four-forms are found to exhibit quite simple
behaviors, though we are not able to derive them in full generality.
