Question

I hope, this question isn't too broad or vague.

In a recent paper, Ognyan Oreshkov et al. worked out a theory of quantum correlations in absence of any causal order, dropping the assumptions of a space-time: See their paper here.

Now I wonder (please refer to the linked paper), would it even be possible to define a Hamiltionian in absence of a space-time to refer to? And if so, how would one do that?

Answer 1

I'll be sure to look all this up when I have more time. However, as the the formulation is completely local, the validity of a Hamiltonian does become less clear
The Hamiltonian is the generator of time-translations. If you eliminate time from the description no true Hamiltonian can exist.