Mathematical structure of dual amplitudes

Abstract

Firstly, the notion of duality is introduced and the generalized amplitude given in terms of the Koba - Nielsen variables. Furthermore, from the point of view of wave functions it is shown how the dynamical importance of spin implies an internal structure or extended description of hadrons which may be linked with duality (or internal symmetry),Then, in the following chapter, we first of all describe how certain mathematical characteristics emerge as being desirable for a strong interaction theory and indicate how these appear in various models, the relationships between which we also explain. It then appears that the most suitable language in which to discuss these properties is that of two-dimensional Riemann surfaces, which are most prominent in the Analogue Model. Chapter III indicates how the structure in dual models may be simply derived without an explicit physical interpretation (as in the functional integral formalism) - Ramond's Correspondence Principle. In the final chapter we propose an approach which embodies the surface description and the mathematical attributes mentioned above (without a tachyon). Furthermore, it amounts to an extended description of interacting hadrons, which, when reconciled with Poincare invariance, leads to the internal symmetry group of the original models.