Quantization of the Order-Parameter Field in Dynamical Spacetime

Reference [5] established the canonical quantization and path-integral quantization schemes for the order-parameter field in static spacetime. This paper generalizes these schemes to general dynamical spacetimes, addresses the non-uniqueness of positive-frequency modes and Bogoliubov transformations in dynamical backgrounds, and establishes a complete field-theoretic description of particle production and the information dissipation tensor. There are four core results. First, it is proved that the construction of the CTP generating functional is itself covariant and does not rely on the static assumption. Second, the adiabatic vacuum scheme is adopted to resolve the problem of positive-frequency mode selection in dynamical spacetime; an explicit expression for the Bogoliubov coefficients is given; it is proved that the Bogoliubov coefficients are determined by the coupling between the dynamical evolution of the order-parameter field and the information dissipation tensor; and a gravity-dissipation interference effect is discovered that constitutes an exclusive prediction of the Order Parameter Spacetime Theory relative to pure general relativity. Third, the low-frequency limit of the information dissipation tensor in dynamical spacetime and its back-reaction effects are derived; the Bogoliubov-dissipation self-consistent equations are established; and it is proved that the energy dissipation rate of the order-parameter field equals the energy integral of the particle production rate. Fourth, the dynamical generalization of the information dissipation tensor provides a unified quantum field theory foundation for the dynamical evolution of dark energy, the exit from inflation, and the reheating process. In the static limit, all results of this paper rigorously recover the established conclusions of Ref. [5].