Interaction of linear systems with massless quantum fields: inequivalent representations of the canonical commutation relations

A general theoretical framework is developed for the treatment of a class of quantum field theories which are algebraically exactly solvable but which entail the use of non-Fock representations of the CCR algebra for the formulation of scattering theory. It is shown that the nontrivial representation-theoretic considerations are necessitated by phenomena which occur at small momenta in the scattering of massless particles; in this sense the theories model the infrared problem in quantum electrodynamics. Explicit, easily verifiable criteria are developed which select representations amenable to the formulation of Moeller wave operators. One of two major result is the development of necessary and sufficient conditions for the concurrent unitary implementation of two automorphism groups in a class of quasi-free representations of the CCR algebra. The second results is the demonstration that among exactly-solvable systems there are physically reasonable examples for which the selection of a representation to accommodate scattering theory is a nontrivial problem