More on Heisenberg's model for high energy nucleon-nucleon scattering

We revisit Heisenberg's model for nucleon-nucleon scattering which admits a saturation of the Froissart bound. We examine its uniqueness, and find that up to certain natural generalizations, it is the only action that saturates the bound. We find that we can extract also sub-leading behaviour for $\sigma_{\rm tot}(s)$ from it, though that requires a knowledge of the wavefunction solution that is hard to obtain, and a black-disk model allows the calculation of $\sigma_{elastic}(s)$ as well. The wavefunction solution is analyzed perturbatively, and its source is interpreted. Generalizations to several mesons, addition of vector mesons, and curved space regimes are also found. We discuss the relations between Heisenberg's model and holographic models that are dual to QCD-like theories.