Feynman-Like Diagrams Compatible with Duality. I. Planar Diagrams

We propose a perturbative approach in which the Veneziano representation plays the role of a Born term. We interpret Veneziano's formula as describing only the contribution of one-particle intermediate states. We then add to it the contribution of many-particle intermediate states by means of Feynman-like diagrams. The rules for writing the integrals corresponding to any planar diagram are given. Crossing symmetry, duality, and Reggeization are explicitly taken into account. We find the asymptotic behavior of each Feynman-like diagram. We sum them and prove that the whole amplitude has Regge behavior. The new trajectory, however, is no longer linear, and it incorporates correctly the elastic unitarity constraint. We argue that this approach will ultimately provide a framework in which generalized unitarity (in Cutkosky's sense) can be imposed.