Bethe-Salpeter Approach to the Multi-Regge Bootstrap

A Bethe-Salpeter model is proposed which sums graphs that are very similar to those summed in the work of Chew, Goldberger, and Low. This model yields considerably simpler equations and allows the analytic continuation of the amplitude into the angular momentum plane. This model is used to perform the bootstrap calculation for several input trajectories, including the $\rho$ and the Pomeranchuk trajectory. When linear trajectories are assumed, we obtain self-consistent values of the intercept at $t=0\mathrm{}$ that are in the neighborhood of 0.6. The off-shell Bethe-Salpeter wave function is bootstrapped as well as the residue of the pole at $t=0\mathrm{}$.