Infrared divergences in a model related to the Heisenberg algebra

A model describing a trilinear interaction of an infinite-component massive fermion field with two massless scalar fields is proposed. The symmetry of the interaction is related to the Heisenberg algebra. The asymptotic Hamiltonian is exactly diagonalized in the sector containing one massive particle, and the properties of the resulting representations of the canonical commutation relations of the massless fields are discussed.