Dispersion theoretic perturbation methods

Abstract

The manuscript is organized as follows. In Chapter 1 the Chew-Mandelstam equations are derived and there is a general discussion of the partial wave disperison relations and the ODD ambiguity. The dispersion theoretic method of Dashen and Frautschi is presented in Chapter 2 both for single as well as multi channel case. PATCH's investigation of the Dashen-Frautschi method is reviewed in Chapter 5.One of the criticisms concerned the poor convergence of the equations in the presence of short range forces, while the other dealt with the problem of including contributions coming from infra-red divergent terms in the input to the DF expressions. In order to handle the first difficulty a method of modified perturbed dispersion relations is presented and applied to a model calculation in potential theory with good results. A modified Pagels-type procedure to solve the resulting equations for N and D functions is employed. This procedure is then applied to investigate the modified perturbed dispersion relations technique in the presence of long range forces. All this is done in Chapter 4.The modified Pagels-type procedure is employed in Chapter 5 to generate Regge trajectories, the object being to see whether reasonable it is possible to Reggeize the direct channel while using unreggeized input in the crossed channels' is shown that this is possible provided the cut-off is chosen suitably. In Chapter 6 the problem of infra-red divergent contributions to the input in the Dashen-Frautschi method is again treated along the lines of a suggestion due to SQUIRES. The procedure is carried out within the context of potential theory where it is shown to give satisfactory results. The full details of the method are exposed in an Appendix to this Chapter.