  We introduce the holonomy-diffeomorphism algebra, a C*-algebra generated by
flows of vectorfields and the compactly supported smooth functions on a
manifold. We show that the separable representations of the
holonomy-diffeomorphism algebra are given by measurable connections, and that
the unitary equivalence of the representations corresponds to measured gauge
equivalence of the measurable connections. We compare the setup to Loop Quantum
Gravity and show that the generalized connections found there are not contained
in the spectrum of the holonomy-diffeomorphism algebra in dimensions higher
than one. This is the second paper of two, where the prequel gives an
exposition of a framework of quantum gravity based on the
holonomy-diffeomorphism algebra.
