  We construct a generalised formalism for group field theories, in which the
domain of the field is extended to include additional proper time variables, as
well as their conjugate mass variables. This formalism allows for different
types of quantum gravity transition amplitudes in perturbative expansion, and
we show how both causal spin foam models and the usual a-causal ones can be
derived from it, within a sum over triangulations of all topologies. We also
highlight the relation of the so-derived causal transition amplitudes with
simplicial gravity actions.
