Formulate renormalization procedures for fundamental CQ theories that preserve complete positivity

Develop renormalization schemes for fundamental classical–quantum (CQ) path-integral theories that preserve complete positivity and normalization of the dynamics under the introduction of counterterms and running couplings.

Background

While the presented CQ gravity–scalar theory is argued to be an effective theory, the paper highlights the broader open issue of renormalizing fundamental CQ theories. Preserving CP under renormalization may entail subtleties absent in unitary QFTs, especially in open quantum contexts.

A CP-preserving renormalization framework would be essential for any attempt to treat CQ dynamics as fundamental and would clarify how bra–ket structures and classical back-reaction interact with loop corrections.