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Adiabatic Klein-Gordon Dynamics for the Renormalized Nelson Model
Morris Brooks, David Mitrouskas
https://arxiv.org/abs/2509.14226 https://arxiv.org/pdf/25…

Adiabatic Klein-Gordon Dynamics for the Renormalized Nelson Model
We study the renormalized Nelson model in a semiclassical regime where the field becomes classical while the particle remains quantum. The degree of classicality is measured by a small parameter $\varepsilon \ll 1$. In this scaling the particle evolves on microscopic times, whereas the field exhibits nontrivial dynamics only on the macroscopic scale $t=\mathcal{O}(\varepsilon^{-2})$. The natural semiclassical model is the coupled Schrödinger-Klein-Gordon (SKG) system, which encodes the time-sc…