The unbinding transition of the bipolaron

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This project is a part of a larger enterprise aimed at the mathematical understanding of a few particles coupled to a bosonic field. An important subject in this area is the investigation of scattering processes involving charged particles. Due to the infrared problem, rigorous study of such processes requires subtle functional-analytic methods. Efficient techniques to deal with the infrared problem have been developed in relativistic (algebraic) quantum field theory. In particular, they do not require the use of an infrared cut-off at intermediate stages of the argument. In our research project we plan to apply these methods to models of non-relativistic quantum electrodynamics, where scattering theory is not yet fully under control. Our investigations will offer a fresh look at the problem of asymptotic completeness in these models.