Investigations into dual resonance models

Abstract

This thesis is concerned with dual resonance models, especially the Neveu-Schwarz and Ramond Models. The first chapter is an introduction to the subject of dual models and is concerned with the concepts that lead to them and early ideas of dual models. Chapter two presents, in the operator formalism, the Conventional Dual Model and then the Neveu-Schwarz and Eamond Models and is meant to indicate the more important features of these models. The: first part of chapter three deals with the string pictures of dual models and various ways of considering dual models which can be considered to be related to the string pictures. The latter half of chapter three deals with the formulation of the Neveu-Schwarz Model by the use of a finite Grassmann algebra which extends the Conventional Dual Model, in Koba-Nielsen variables, directly into the Neveu-Schwarz Model. The tree graph and one loop diagrams are calculated explicitly while the form for higher order terms is given in terms of automorphic functions. The first part of chapter four presents a method of obtaining the functions, involved in one loop meson and fermion diagrams with external mesons, by the use of Neumann functions on an annulus, the boundary conditions on the annulus giving the different loop diagrams. The second part of chapter four deals with, the calculation of the Neumann function for one loop diagrams with external fermions and an attempt to obtain the partition function which is necessary to write down the complete amplitude at the one loop level. Chapter four is completed by the construction of the one loop amplitude for four external fermions.