Study of some elementary particle interactions with special reference to the use of stochastic methods

Abstract

This thesis consists of three parts, viz., (i) Better understanding in the methods of Electrodynamic calculations, (ii) Dispersion theory -recent techniques and applications and (iii) Particle physics - phenomenological approach, an illustration. These three parts concerns with the study of processes which illustrate the nature and scope of the attempts with particular emphasis on a critical examination of the physical basis of quantum field theory. It is ascertained that the study of interactions within the frame work of perturbation expansions is not only conceptually satisfying but bears an elegant correspondence with the description of evolutionary stochastic processes. It leads to the derivation of the field operators. Hence the physical basis of quantum field theory is built on an interpretation of the integrand of the S-matrix. It is believed that this attempt is no ta mere reformulation of known axioms since it leads to a new proof of the equivalence between the Feynman and field theoretic formalisms. The Feynman propagator is decomposed into positive and negative energy parts; The relative contributions from the two parts to the matrix element for electrodynamic processes like Compton scattering and Bremmstrahlung are calculated. The equivalence between the energy denominators occuring in the field theoretic formalism and the method of the decomposed Feynman propagator are demonstrated respectively, by identifying the energy denominators in the two formalisms upto fourth order perturbation expansions. A generalized proof for the nth order also is given. Part II of this thesis consists of an application of the recent developments in dispersion theoretic techniques to various problems involving strange particles.