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 fa mily of involutions in A(R) and construct the relative Fock representa tions, examining the positivity of the metric. As an application of th e general results, we rigorously prove unitarity of the scattering ope rator of integrable models in 1+1 space-time dimensions. In this conte xt the possibility of adopting various involutions in the Zamolodchiko v-Faddeev algebra is also explored. (C) 1997 American Institute of Phy sics.