Self-adjointness and domain of generalized spin-boson models with mild ultraviolet divergences

TL;DR

This paper rigorously constructs a broad class of generalized spin-boson models with mild ultraviolet divergences, providing explicit formulas for their self-adjoint domains, applicable to multi-atom systems with finite energy levels.

Contribution

It introduces a new rigorous construction method for spin-boson models with mild ultraviolet divergences, including explicit domain formulas for the Hamiltonians.

Findings

Constructed a large class of spin-boson models with ultraviolet divergences.

Provided explicit formulas for the domain of self-adjointness.

Applicable to models with multiple atoms and finite energy levels.

Abstract

We provide a rigorous construction of a large class of generalized spin-boson models with ultraviolet-divergent form factors. This class comprises various models of many possibly non-identical atoms with arbitrary but finite numbers of levels, interacting with a boson field. Ultraviolet divergences are assumed to be mild, such that no self-energy renormalization is necessary. Our construction is based on recent results by A. Posilicano, which also allow us to state an explicit formula for the domain of self-adjointness for our Hamiltonians.