Modular wedge localization and the d=1+1 formfactor program

In this paper I continue the study of the new Framework of modular localization and its constructive use in the nonperturbative d=1+1 Karowski-Weisz-Smirnov formfactor program. Particular attention is focussed on the existence of semilocal generators of the wedge-localized algebra without vacuum polarization (FWG-operators), which are closely related to objects fulfilling the Zamolodchikov-Faddeev algebraic structure. They generate a "thermal Hilbert space" and allow us to understand the equivalence of the KMS conditions with the so-called cyclicity equation for formfactors, which are known to be closely related to crossing symmetry properties. The modular setting gives rise to interesting new ideas on "free" d=2+1 anyons and plektons. (C) 1999 Academic Press.