  We link the notion causality with the orientation of the 2-complex on which
spin foam models are based. We show that all current spin foam models are
orientation-independent, pointing out the mathematical structure behind this
independence. Using the technology of evolution kernels for quantum
fields/particles on Lie groups/homogeneous spaces, we construct a generalised
version of spin foam models, introducing an extra proper time variable and
prove that different ranges of integration for this variable lead to different
classes of spin foam models: the usual ones, interpreted as the quantum gravity
analogue of the Hadamard function of QFT or as a covariant definition of the
inner product between quantum gravity states; and a new class of causal models,
corresponding to the quantum gravity analogue of the Feynman propagator in QFT,
non-trivial function of the orientation data, and implying a notion of
''timeless ordering''.
