The infrared problem consists in the divergence of certain integrals for small momenta in quantum field theory, notably in QED. It is believed that one of the reasons for this problem is the appearance of non-Fock representations of canonical commutation relations. I will describe a class of simple but non-trivial models, studied recently by C. Gerard and myself, for which one can show rigorously the existence of non-Fock asymptotic fields. I will describe a number of open problems concerning these models.
Heinz Siedentop