  The Lambda-renormalized Einstein-Schrodinger theory is a modification of the
original Einstein-Schrodinger theory in which a cosmological constant term is
added to the Lagrangian, and it has been shown to closely approximate
Einstein-Maxwell theory. Here we generalize this theory to non-Abelian fields
by letting the fields be composed of dxd Hermitian matrices. The resulting
theory incorporates the U(1) and SU(d) gauge terms of
Einstein-Maxwell-Yang-Mills theory, and is invariant under U(1) and SU(d) gauge
transformations. The special case where symmetric fields are multiples of the
identity matrix closely approximates Einstein-Maxwell-Yang-Mills theory in that
the extra terms in the field equations are 10^-13 of the usual terms for
worst-case fields accessible to measurement. The theory contains a symmetric
metric and Hermitian vector potential, and is easily coupled to the additional
fields of Weinberg-Salam theory or flipped SU(5) GUT theory. We also consider
the case where symmetric fields have small traceless parts, and show how this
suggests a possible dark matter candidate.
