  Building on the results of previous work, we demonstrate how matter fields
are incorporated into the general linear frame approach to general relativity.
When considering the Maxwell one-form field, we find that the system that leads
naturally to canonical vierbein general relativity has the extrinsic curvature
of the Cauchy surface represented by gravitational as well as non-gravitational
degrees of freedom. Nevertheless the metric compatibility conditions are
undisturbed, and this apparent derivative-coupling is seen to be an effect of
working with (possibly orthonormal) linear frames. The formalism is adapted to
consider a Dirac Fermion, where we find that a milder form of this apparent
derivative-coupling appears.
