Fock representations of exchange algebras with involution

An associative algebra A R with exchange properties generalizing the canonical (anti)commutation relations is considered. We introduce a family of involutions in A R and construct the relative Fock representations, examining the positivity of the metric. As an application of the general results, we rigorously prove unitarity of the scattering operator of integrable models in 1+1 space-time dimensions. In this context the possibility of adopting various involutions in the Zamolodchikov–Faddeev algebra is also explored.