Renormalization and loop corrections in the CQ Yukawa model

Develop a renormalization procedure to consistently handle self-energy and loop diagrams in the classical–quantum Yukawa model’s influence functional and propagators, including finite-width effects induced by the D0 and D2 terms, so that dynamics beyond tree level and forward scattering can be treated within the CQ framework.

Background

In deriving the influence functional, the authors focus on cross terms and omit self-interaction contributions (e.g., J_i J_i) to restrict attention to tree-level 2→2 scattering. They note, however, that loop and self-energy effects are important and will differ from standard unitary quantum field theory because the CQ model introduces decoherence and diffusion, implying finite widths and non-unitary corrections.

They explicitly state that dealing with these loop effects requires a renormalization approach suitable for the CQ setting and defer this analysis, pointing to related discussion in contemporaneous work.