arXiv:2508.00803

Renormalization of generalized spin-boson models with critical ultraviolet divergences

Benjamín Álvarez, Sascha Lill, Davide Lonigro, Martín, Javier Valentín

Published Aug 1, 2025• 0 citations

Abstract

We provide a rigorous construction of generalized spin--boson models with commuting transition matrices and form factors exhibiting critical ultraviolet (UV) divergences. That is, we cover all divergences where a self-energy renormalization, but no non-Fock representation, is required. Our method is based on a direct definition of the renormalized Hamiltonian on a sufficiently large test domain, followed by a Friedrichs extension. We then prove that this Hamiltonian coincides with the one obtained by cut-off renormalization. Furthermore, we show that for specific supercritical cases, i.e., when a non-Fock representation is required, the renormalized Hamiltonian is trivial.

DOI: 10.48550/arxiv.2508.00803

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