Studies of the mathematical properties Regge-pole and dual amplitudes are important both for their applications in high energy phenomenology generalizations to strings, superstrings, branes, other theoretical developments. In present paper, we investigate similarities differences between two classes amplitudes: one with Mandelstam analyticity (DAMA) another logarithmic trajectories (Dual-log). ...

In these lectures I review classical aspects of the self-dual Chern-Simons systems which describe charged scalar fields in 2 + 1 dimensions coupled to a gauge field whose dynamics is provided by a pure Chern-Simons Lagrangian. These self-dual models have one realization with nonrelativistic dynamics for the scalar fields, and another with relativistic dynamics for the scalars. In each model, th...

No reliable analytic approach exists to QCD at large distances. The usual perturbative quantization leads to an S matrix which is not Borel summable. For reasons which are not understood the perturbative expansion works anyhow at small distances, where a few terms correctly describe experiments. It fails at large distances, where the coupling is large, in particular in describing confinement of...