Ballesteros, Miguel; Deckert, DirkAndre; Haenle, Felix
(2020):
Oneboson scattering processes in the massless SpinBoson model  A nonperturbative formula.
In: Advances in Mathematics, Vol. 371, 107248

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Abstract
In scattering experiments, physicists observe socalled 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 welldeveloped 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 nonperturbative formula that relates the scattering matrix to the resolvent operator in the massless SpinBoson model. This result can be seen as a major progress compared to our previous works [14] and [12] in which we only managed to derive a perturbative formula.