Renormalization of spin$\unicode{x2013}$boson interactions mediated by singular form factors

TL;DR

This paper extends the rotating-wave spin-boson model to include singular form factors, developing a rigorous renormalization method and operator construction for these more general interactions.

Contribution

It introduces a novel renormalization framework for spin-boson models with singular form factors, broadening the class of interactions that can be rigorously analyzed.

Findings

Successfully constructs annihilation and creation operators for singular form factors.

Provides a rigorous renormalization procedure for non-normalizable interactions.

Extends the mathematical understanding of spin-boson models with singular couplings.

Abstract

We study and discuss the extension of the rotating-wave spin$\unicode{x2013}$boson model, together with more general models describing a system$\unicode{x2013}$field coupling with a similar rotating-wave structure, to interactions mediated by possibly singular (non-normalizable) form factors satisfying a weaker growth constraint. To this purpose, a construction of annihilation and creation operators as continuous maps on a scale of Fock spaces, together with a rigorous renormalization procedure, is employed.