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

Review of Recent Work on Narrow Resonance Models

“…The calculation reproduces the result of and of Bardakci, Halpern, and Shapiro (1969). Thorn and Kaku (1969) have used the harmonic oscillator formalism of Fubini, Gordan, and Veneziano (1969) and the twisting operator of Caneschi, Schwimmer, and Veneziano (1969) Kikkawa, Klein, Sakita, and Virasoro (1969).…”

Dual Resonance Theory with Nonlinear Trajectories

“…But the insight into Regge poles provided by the models of 12 13 Van Hove , and an additional finite number of s-channel pole terms which are not present in (2), the amplitude will then possess polynomial t dependence. In general, the asymptotic t behavior of (2) is s dependent and cannot cancel an additive polynomial in t. Therefore, if we demand that the Born term be well behaved at small fixed s and large t, the only s-channel pole terms which might not be included in (2) would be s-wave terms.…”

General trees and general loops in the unitarization of the dual resonance model

“…The idea of uni tarization of the dual resonance model, as suggested· by the factorization propert; of n-point Veneziano formula, is to regard the n-point Veneziano ampli1;:.ude as the Born (or tree) amplitude, Which is an a~~roximation 6 to a more exact physical scattering ~lllplitude.. One then attempts to construct, from unitarity, the higher order multiloop amplitudes, co~patible 6 with theduality assumption~ In other words, the unitarity constraint is im!>osed on the dual ·resonance model in a perturbative way, strictly in analogy with the .perturbativefielq. theory.…”