Non-Trivial Renormalization of Spin-Boson Models with Supercritical Form Factors
Mathematical Physics
2026-03-11 v3 Functional Analysis
math.MP
Abstract
In this paper we construct the non-trivial, renormalized Hamiltonian for a class of spin-boson models with supercritical form factors, including the one describing the Weisskopf-Wigner spontaneous emission. The renormalization is performed through both a self-energy and mass renormalization, in the so-called Hamiltonian formalism of constructive quantum field theory, implemented by a non-unitary dressing transformation. This solves the problem of triviality for unitarily-renormalized supercritical spin-boson models.
Cite
@article{arxiv.2508.00805,
title = {Non-Trivial Renormalization of Spin-Boson Models with Supercritical Form Factors},
author = {Marco Falconi and Benjamin Hinrichs and Javier Valentín Martín},
journal= {arXiv preprint arXiv:2508.00805},
year = {2026}
}
Comments
The paper is now superseded by arXiv:2603.07045 (written by the same authors), that in particular contains a stronger version of the results appeared here, and new ones