We establish a precise relation between the integral kernel of the scattering matrix and the resonance in the Spin-Boson model, which describes the interaction of a two-level quantum system with a second-quantized scalar field. For this purpose, we derive an explicit formula for the two-body scattering matrix. This provides a mathematical framework for the peaks at certain energy values in the scattering cross-section that physicists have observed since the beginning of quantum mechanics. In the case of quantum mechanics, this problem was addressed in numerous works that culminated in Simon’s seminal paper (Ann Math, 1973). However, in quantum field theory, the analogous problem was open for several decades at the level of rigor required in mathematics.
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