Adiabatic Klein–Gordon dynamics for the renormalized Nelson model Brooks, Morris ; https://orcid.org/0000-0002-6249-0928 Mitrouskas, David Johannes ddc:500 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 ε << 1. In this scaling the particle evolves on microscopic times, whereas the field exhibits nontrivial dynamics only on the macroscopic scale t = O(ε^−2). The natural semiclassical model is the coupled Schrödinger–Klein–Gordon (SKG) system, which encodes the time-scale separation through an explicit ε-dependence. Based on this scale separation in SKG, we apply the adiabatic principle to derive a new PDE for the classical field, the ε-free adiabatic Klein–Gordon (aKG) equation, where the field is driven by the instantaneous ground state of the particle. Our main result is a norm approximation of the Nelson dynamics by the aKGsolution corrected by a quasi-free fluctuation dynamics around the classical field, generated by a renormalized Bogoliubov–Nelson Hamiltonian. As a corollary, we obtain convergence of the reduced one-body densities for both subsystems, where the fluctuation correction vanishes, thereby justifying aKG as a semiclassical Born–Oppenheimer type approximation of the renormalized Nelson model. Springer 2026 info:eu-repo/semantics/article doc-type:Article Article http://purl.org/coar/resource_type/c_2df8fbb1 https://research-explorer.ista.ac.at/record/23153 https://research-explorer.ista.ac.at/download/23153/23166 Brooks M, Mitrouskas DJ. Adiabatic Klein–Gordon dynamics for the renormalized Nelson model. <i>Calculus of Variations and Partial Differential Equations</i>. 2026;65(10). doi:<a href="https://doi.org/10.1007/s00526-026-03436-9">10.1007/s00526-026-03436-9</a> eng info:eu-repo/semantics/altIdentifier/doi/10.1007/s00526-026-03436-9 info:eu-repo/semantics/altIdentifier/issn/0944-2669 info:eu-repo/semantics/altIdentifier/e-issn/1432-0835 info:eu-repo/semantics/altIdentifier/arxiv/2509.14226 info:eu-repo/semantics/altIdentifier/pmid/42865432 info:eu-repo/semantics/openAccess