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 F(S). It is associated with a given two-particle S-matrix and has the following features: (i) It contains a double TTS algebra as a subalgebra. (ii) Form factors arise as thermal vector states over F(S) of temperature 1/2π. 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 spacetime. In F(S) it is manifest through modular structures (j, δ) in the sense of algebraic QFT, which can be implemented explicitly in terms of the TTS generators.