  In this paper we introduce an equivariant extension of the Chern-Simons form,
associated to a path of connections on a bundle over a manifold M, to the free
loop space LM, and show it determines an equivalence relation on the set of
connections on a bundle. We use this to define a ring, loop differential
K-theory of M, in much the same way that differential K-theory can be defined
using the Chern-Simons form [SS]. We show loop differential K-theory yields a
refinement of differential K-theory, and in particular incorporates holonomy
information into its classes. Additionally, loop differential K-theory is shown
to be strictly coarser than the Grothendieck group of bundles with connection
up to gauge equivalence. Finally, we calculate loop differential K-theory of
the circle.
