  We give parallel constructions of an invariant R(W,f), based on the classical
Rogers dilogarithm, and of quantum hyperbolic invariants (QHI), based on the
Faddeev-Kashaev quantum dilogarithms, for flat PSL(2,C)-bundles f over closed
oriented 3-manifolds W. All these invariants are explicitely computed as a sum
or state sums over the same hyperbolic ideal tetrahedra of the idealization of
any fixed simplicial 1-cocycle description of (W,f) of a special kind, called a
D-triangulation. R(W,f) recovers the volume and the Chern-Simons invariant of
f, and we conjecture that it determines the semi-classical limit of the QHI.
