Constructive proposals for QFT based on the crossing property and on lightfront holography

The recent concept of modular localization of wedge algebras suggests two methods of classifying and constructing QFTs, one based on particle-like generators of wedge algebras using on-shell concepts (S-matrix, formfactors: crossing property) and the other using the off-shell simplification of lightfront holography (chiral theories). The lack of an operator interpretation of the crossing property is a serious obstacle in on-shell constructions. In special cases, one can define a “masterfield” whose connected formfactors constitute an auxiliary thermal QFT for which the KMS cyclicity equation is identical to the crossing property of the formfactors of the master field. Further progress is expected to result from a conceptual understanding of the role of on-shell concepts as particle states and the S-matrix within the holographic lightfront projection.