2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/93715It is shown that the connection form (gauge field) related to the generalization of the Berry phase to mixed states proposed by Uhlmann satisfies the source-free Yang-Mills equation *D*Dw=0, where the Hodge star is taken with respect to the Bures metric on the space of finite dimensional nondegenerate density matrices.6 pages, LatexQuantum PhysicsMathematical Physicstext