Infrared singular fields and nonregular representations of canonical commutation relation algebras

Infrared singular variables which often enter in the formulation of models in quantum field theory, many-body theory, and quantum statistical mechanics are described in terms of nonregular representations of canonical commutation relations algebras. General properties of such representations are discussed. In this way one also obtains insight into the construction and representation of charged field algebras 𝒜 as canonical extensions of a neutral (observable) algebra 𝒜0. The charged state representations of 𝒜0 are obtained through nonregular vacuum representations of the extended field algebra 𝒜. The above structures are proven to work in several explicit models.