Integrable QFT and Longo-Witten endomorphisms (Q2256020)

Integrable quantum field theories in \(1+1\) dimensions have recently become amenable to a rigorous construction, but many questions about the structure of their local observables remain open. In present paper the authors construct quantum field models in the two-dimensional spacetime; they extend previous constructions of Borchers triple to massless scattering with nontrivial left and right components. A massless Borchers triple is constructed from a set of left-left, right-right and left-right scattering functions. They find a correspondence between massless left-right scattering \(S\)-matrices and massive block diagonal \(S\)-matrices. Finally, they point out a simple class of \(S\)-matrices with examples, and study the restriction of two-dimensional models to the lightray. Several arguments for constructing strictly local two-dimensional nets are presented and possible scenarios are discussed.