UCLA

In this dissertation we describe several recent advancements in the study of Coon amplitudes.

In the first chapter, we detail the properties of the Veneziano, Virasoro, and Coon amplitudes. These tree-level four-point scattering amplitudes may be written as infinite products with an infinite sequence of simple poles. Our approach for the Coon amplitude uses the mathematical theory of q-analysis. We interpret the Coon amplitude as a q-deformation of the Veneziano amplitude for all q ≥ 0 and discover a new transcendental structure in its low-energy expansion. We show that there is no analogous q-deformation of the Virasoro amplitude.

In the second chapter, we analyze so-called generalized Veneziano and generalized Virasoro amplitudes. Under some physical assumptions, we find that their spectra must satisfy an over-determined set of non-linear recursion relations. The recursion relation for the generalized Veneziano amplitudes can be solved analytically and yields a two-parameter family which includes the Veneziano amplitude, the one-parameter family of Coon amplitudes, and a larger two-parameter family of amplitudes with an infinite tower of spins at each mass level. In the generalized Virasoro case, the only consistent solution is the string spectrum.