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

Understand

The crossing property is perhaps the most subtle aspect of the particle-field relation.

• Although it is not difficult to state its content in terms of certain analytic properties relating different matrixelements of the S-matrix or formfactors, its relation to the localization- and positive energy spectral principles requires a level of insight into the inner workings of QFT which goes beyond anything which can be found in typical textbooks on QFT.
• This paper presents a recent account based on new ideas derived from "modular localization" including a mathematic appendix on this subject.
• Its main novel achievement is the proof of the crossing property of formfactors from a two-algebra generalization of the KMS condition.