Discrete quantum gravity, isometric dynamics
We show that if a discrete quantum gravity is not classical, then it cannot be generated by an isometric dynamics. In particular, we show that if the quantum measure µ (or equivalently the decoherence functional) is generated by an isometric dynamics, then there is no interference between events so the system describing evolving universes is classical. The result follows from a forbidden configuration in the path space of causal sets.
Gudder, S., "Discrete Quantum Gravity is not Isometric" (2011). Mathematics Preprint Series. 34.