  We show that Quillen's formalism for computing the Chern character of the
index using superconnections extends to arbitrary operators with functional
calculus. We thus remove the condition that the operators have, up to homotopy,
a gap in the spectrum. This is proved using differential graded algebras and
non-commutative differential forms. Our results also give a new proof of the
coincidence of the Chern character of a difference bundle defined using
super-connections with the classical definition.
