I’m in the process of drafting a paper on resolving the problems associated with Haag’s theorem: Haag, R. (1955). “On quantum field theories,” Matematisk-fysiske Meddelelser, 29, 12.
This involves resurrecting direct-action theories as a possible account of how Nature really works. It is perhaps not well known that John Wheeler himself was attempting to resurrect the direct action approach in 2003, together with his colleague Daniel Wesley (“Towards an Action-at-a distance concept of spacetime”, in A. Ashtekar et al, (2003) Revisiting the Foundations of Relativistic Physics, Kluwer, 421-436). In this piece, Wheeler and Wesley not only speak favorably of the Wheeler-Feynman theory of electrodynamics but recommend applying the same basic approach to quantum gravity. So perhaps, reports of the alleged demise of direct action theories have been premature. Comments welcome, especially if you have a concern that you think should be addressed in such a paper.
The relation of Haag’s theorem to the adequacy of the assumption of the unitary S-Matrix in the black hole information problem, firewalls, fireworks and and all that.
Penrose and Hawking originally were quite ready to accept non-unitarity of the S-Matrix in quantum gravity. Hawking caved in to Susskind prematurely in my opinion. The unitary non-equivalence of QFT vacua in several areas of physics seems to require a re-evaluation of the unitarity axiom especially since the collapse view of strong Von-Neumann projection operator measurement, in contrast of weak pre and post-selected measurements, is non-unitary. Indeed, all open systems are non-unitary and the causal-diamond describing our observable universe bounded by the past particle and the future de Sitter event horizons is not a closed thermodynamic system. The basic idea that unitarity is needed to conserve information at the fundamental level is itself suspect. The Second Law of thermodynamics even in a closed system does not generally conserve entropy.