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?