It's hard for me to tell if the Causal set theory is a quantum field theory of QG. There really isn't that much information on the subject.
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Causal set theory is an approach to quantum gravity which models events on 4 dimensional space time manifolds as points in partially ordered sets where the relation is causality in the sense of events having happened before or after others in time. I suggest checking out this living review for a foray into the subject.
Whilst the subject is still young within the area of matter fields, path integral approaches have been explored extensively.
Jake Xuereb
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