The unitary equation in a fixed momentum transfer representation

An extension of the fixed momentum transfer representation for an S-matrix representation of elementary particles is developed. In this representation it is postulated that a function S_U⁽²⁾ on the second sheet can be found such that the matrix product SS_U⁽²⁾ is analytic everywhere in a complex energy plane, and S_U⁽²⁾ is a continuation of $\text{S}{}^1$ in the neighborhood of the right-hand cut. The problem of π⁺p scattering is considered. The kinematic variables are continued from the physical region to the neighborhood of the Born pole, and the unitary equation is there applied. A function for S_U⁽²⁾ was chosen there with parameters determined by unitarity. Two calculations were made, each with a different choice for the form of S_U⁽²⁾. It is shown how unitarity determines the coupling constant together with the values of the parameters of S_U⁽²⁾. The calculated value of the coupling constant, in both cases, is ～ 16, in good agreement with experiment.