Quantum Field Theory Foundations of Order Parameter Spacetime

We establish rigorous quantum field-theoretic foundations for the order parameter spacetime theory. Starting from the unified action of Ref. [2], we perform canonical and path-integral quantization of the order parameter field in curved spacetime, and establish the equivalence between the Schwinger–Dyson equations and the CTP effective action framework. We generalize the fluctuation–dissipation theorem to general curved spacetimes at finite temperature, and use the Schwinger–DeWitt expansion to explicitly determine the back-reaction coefficients c₁ and c₂ in the geometric feedback equation of Ref. [4], finding that they diverge near the critical point of the order parameter. We derive the information energy–momentum tensor by rigorous metric variation, proving that the constructive ansatz of Ref. [4] is the inevitable one-loop result, thus elevating it to a theorem. We introduce fermionic matter fields and provide a quantum field-theoretic expression for the Mach force—the gradient of inertial mass—revealing that it can spontaneously drive inflation and dark energy without additional scalar fields. We verify unitarity, micro-causality, and renormalization self-consistency. With this, the five-paper series of the order parameter spacetime theory is conceptually fully closed. This paper builds upon prior works in the series [10.5281/zenodo.21325459, 10.5281/zenodo.21499343, 10.5281/zenodo.21499696, 10.5281/zenodo.21504738].