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The crossing property is perhaps the most subtle aspect of the particle-fieldrelation. Although it is not difficult to state its content in terms of certainanalytic properties relating different matrixelements of the S-matrix orformfactors, its relation to the localization- and positive energy spectralprinciples requires a level of insight into the inner workings of QFT whichgoes beyond anything which can be found in typical textbooks on QFT. This paperpresents a recent account based on new ideas derived from "modularlocalization" including a mathematic appendix on this subject. Its main novelachievement is the proof of the crossing property of formfactors from atwo-algebra generalization of the KMS condition. The main content of thisarticle is the presentation of the derailments of particle theory during morethan 4 decades: the S-matrix bootstrap, the dual model and its string theoreticextension. Rather than being related to crossing, string theory is the (onlyknown) realization of a dynamic infinite component one-particle wave functionspace and its associated infinite component field. Here "dynamic" means that,unlike a mere collection of infinitely many irreducible unitary Poincar\'egroup representation or free fields, the formalism contains also operatorswhich communicate between the different irreducible Poincar\'e represenations(the levels of the "infinite tower") and set the mass/spin spectrum. Wheras inpre-string times there were unsuccessful attempts to achieve this in analogy tothe O(4,2) hydrogen spectrum by the use of higher noncompact groups, thesuperstring in d=9+1, which uses instead (bosonic/fermionic) oscillatorsobtained from multicomponent chiral currents is the only known unitary positiveenergy solution of the dynamical infinite component pointlike localized fieldproject.

A critical look at 50 years particle theory from the perspective of the crossing property