Numerical Studies of the Bethe-Salpeter Equation and the Multiperipheral Integral Equation of Amati, Bertocchi, Fubini, Stanghellini, and Tonin

We present some numerical results for Regge poles determined from the Bethe-Salpeter equation with scalar couplings. Both the trajectories and residue functions are determined. We find that it is a good approximation to ignore the coupling between different $O\left(4\right)\mathrm{}$ states. The effect of a second-order correction to the potential (the crossed-box graph) is studied and evaluated numerically. The relation of the Bethe-Salpeter equation with the multiperipheral integral equation is reviewed, and we show how to solve the latter equation by numerical iteration. Some results are given which do not exhibit any oscillations in the total cross section.