# One-Boson Scattering Processes in the Massless Spin-Boson Model -- A Non-Perturbative Formula

## TL;DR

This paper derives a non-perturbative formula linking the scattering matrix and resolvent operator in the massless Spin-Boson model, advancing the understanding of resonances in quantum field theory.

## Contribution

It provides the first non-perturbative relation between scattering matrix and resolvent in the massless Spin-Boson model, improving upon previous perturbative results.

## Key findings

- Established a non-perturbative formula for the model
- Connected scattering matrix poles with resolvent operator
- Progressed understanding of resonances in quantum field models

## Abstract

In scattering experiments, physicists observe so-called resonances as peaks at certain energy values in the measured scattering cross sections per solid angle. These peaks are usually associate with certain scattering processes, e.g., emission, absorption, or excitation of certain particles and systems. On the other hand, mathematicians define resonances as poles of an analytic continuation of the resolvent operator through complex dilations. A major challenge is to relate these scattering and resonance theoretical notions, e.g., to prove that the poles of the resolvent operator induce the above mentioned peaks in the scattering matrix. In the case of quantum mechanics, this problem was addressed in numerous works that culminated in Simon's seminal paper [33] in which a general solution was presented for a large class of pair potentials. However, in quantum field theory the analogous problem has been open for several decades despite the fact that scattering and resonance theories have been well-developed for many models. In certain regimes these models describe very fundamental phenomena, such as emission and absorption of photons by atoms, from which quantum mechanics originated. In this work we present a first non-perturbative formula that relates the scattering matrix to the resolvent operator in the massless Spin-Boson model. This result can be seen as a major progress compared to our previous works [13] and [12] in which we only managed to derive a perturbative formula.