Non-Trivial Renormalization of Spin-Boson Models with Supercritical Form Factors

TL;DR

This paper develops a non-trivial renormalized Hamiltonian for supercritical spin-boson models, addressing triviality issues through a self-energy and mass renormalization process within a constructive quantum field theory framework.

Contribution

It introduces a novel renormalization method for supercritical spin-boson models using a non-unitary dressing transformation, solving triviality problems.

Findings

Successfully constructs a non-trivial Hamiltonian for supercritical models

Addresses triviality in unitarily-renormalized models

Provides a framework applicable to Weisskopf-Wigner emission

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.