Yang-Mills fields as optical media

A geometrization of the Yang-Mills field, by which an SU(2) gauge theory be comes equivalent to a 3-space geometry-or optical system-is examined. In a first step, ambient space remains Euclidean and current problems on flat sp ace can he looked at from a new point of view. The Wu-Yang ambiguity, for e xample, appears related to the multiple possible torsions of distinct metri c-preserving connections. In a second step, the ambient space also becomes curved. In the generic case, the strictly Riemannian metric sector plays th e role of an arbitrary host space, with the gauge potential represented by a contorsion. For some field configurations, however, it is possible to obt ain a purely metric representation. In those cases, if the space is symmetr ic homogeneous, the Christoffel connections are automatically solutions of the Yang-Mills equations.