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.

References

Clarifying the steady states of CQ systems and how one computes scattering amplitles in practice, we leave to future work.

— Quantum gravity with dynamical wave-function collapse via a classical scalar field  (2402.17024 - Weller-Davies, 2024) in Section 4: Quantum gravity with dynamical collapse

Moreover, we must take into account the expansion of the Universe to discuss the particle creations which played the important role in the conjecture of the new equilibrium state proposed in . This is crucial to study whether such a new equilibrium state exists or not in our model of the quantum field theory coupling to the semi-stable classical solution in the Higgs potential.

— Instability diagram of the massive gauge quantum fields around the nonlinear massive classical wave solution  (2608.19855 - Kitadono et al., 20 Aug 2026) in Section 6, Conclusion