Inelasticity and partial wave dispersion relations

Abstract

This thesis deals with some general work on the ND(^-1) equations and, more specifically, with two calculations which make use of them. Chapter 1 commences with a brief outline of the subject, followed by a fairly detailed analysis of numerical methods of solution of the equations, including an analysis of cut off and threshold problems. In particular we demonstrate a particular form of numerical solution which appears to be rather superior to any previous ones. Chapter 2 discusses the problems that arise when a multi-channel calculation is approximated to be a single channel one: we show that in general the results are different, and discuss the conditions for them to agree. Chapter 3 investigates what happens when N and D have simultaneous zeroes: it is shown that a potential that leads to this is necessarily singular and repulsive. Chapter 4 opens with a general review of the successes and failures of the quark model in scattering theory. It is shown that the quark model is necessarily inconsistent with what is commonly called bootstrap philosophy, and we investigate whether a reasonably convincing quark model may be constructed. Chapter 5 outlines a calculation of the πN P(_11) phase shift. The previous work on this problem is discussed, and the computational method is outlined along with a discussion of what results can be expected from the calculation.