Abstract
Quantum causal histories are defined to be causal sets with Hilbertspacesattached to each event and local unitary evolution operators. Thereflexivity, antisymmetry and transitivity properties of acausal set are preserved in the quantum history as conditions on theevolutionoperators. A quantum causal history in which transitivity holds can betreated as`directed' topological quantum field theory.Two examples of such histories are described.
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