I've yet to find a limit to this principle 
metaphysical point almost, but it has "computational universe implications." it makes more sense for simulations to have one hamiltonian in one area around a singularity, as it may for nature, now, decide what to do on the edges and to synchronise!
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Any answer to this question will naturally depend on the formalism of QFT you choose to work in. In the geometry-centric pov I like, this sort of question has a natural answer. The first 15 pages of https://people.math.umass.edu/~gwilliam/vol1may8.pdf … may give you a sense
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a basic idea in that approach (congruent with the modern approach to geometry), is that whatever a quantum field theory *is*, it assigns some algebraic datum to an open subset of space-time. Then there is a series of compatibilities for collections open subsets that interact.
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in particular, in QM the algebraic datum assigned to an open subset will include a hamiltonian, valid for that region of space-time; this hamiltonian will act on the Hilbert space of states. The different hamiltonians are related by the topological compatibilities.
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