Characterize CQ asymptotic steady states and define scattering amplitudes in the CQ path-integral framework

Characterize the asymptotic steady states of the classical–quantum dynamics described by the CQ path integral for quantum gravity coupled to a classical scalar field, and develop a concrete prescription for computing scattering amplitudes within this CQ formalism.

Background

In the paper’s CQ model, the classical scalar field interacts dynamically with the quantum metric, leading to non-unitary but completely positive evolution. While the partition function and correlators are formulated, the identification of asymptotic steady states and a practical scattering framework are deferred.

A systematic understanding of steady states and scattering would enable quantitative predictions and comparisons with standard quantum field theory, clarifying the operational meaning of in/out states in CQ dynamics.