Rigorous quantization of the gravitational interaction

Develop a mathematically rigorous quantization of the gravitational interaction, providing a consistent quantum theory of gravity beyond the semiclassical framework of quantum fields on fixed Lorentzian manifolds.

Background

The paper studies the semiclassical Einstein–Klein–Gordon system, explicitly separating it from the full problem of quantum gravity. The authors emphasize that, although semiclassical gravity can be rigorously formulated and analyzed, a complete and mathematically rigorous quantization of gravity itself is still lacking.

This open problem motivates the semiclassical approach taken in the paper, where quantum matter is coupled to classical geometry via the expectation value of the renormalised stress-energy tensor.

References

While a rigorous mathematical quantisation of gravitational interaction remains an open problem, the study of quantum field theory on fixed Lorentzian manifolds has yielded profound structural insights, providing the mathematical foundation for phenomena such as the Hawking effect for spacetime containing black holes and particle creation in the context of cosmological backgrounds .

— The Semiclassical Einstein-Klein-Gordon System: Asymptotic Analysis of Minkowski Spacetime  (2604.01047 - Galanda et al., 1 Apr 2026) in Section 1: Introduction