ELSEVIER Nuclear Physics B 519 [FS] (1998) 517-550 Form factors, thermal states and modular structures

Form factor sequences of an integrable QFT can be defined axiomatically as solutions of a system of recursive functional equations, known as "form factor equations". We show that their solution can be replaced with the study of the representation theory of a novel algebra,)c(S). It is associated with a given two-particle S-matrix and has the following features: (i) It contains a double TI'S algebra s a subalgebra. (ii) Form factors arise as thermal vector states over P (S) of temperature 1/2m The thermal ground states are in correspondence to the local operators of the QFT. (iii) The underlying 'finite temperature structure ' is indirectly related to the "Unruh effect" in Rindler space-time. In.T(S) it is manifest hrough modular structures (j, 8) in the sense of algebraic QFT, which can be implemented explicitly in terms of the TTS generators. @ 199