A BETHE-SALPETER HARMONIC OSCILLATOR FERMION QUARK MODEL FOR MESONS

The purpose of the thesis is to provide a more realistic alternative to the many existing harmonic oscillator quark models while retaining some of the simplicity of their phenomenological versions.;The work divides naturally into three parts. The first part might be termed field theoretic bound state equation transformation theory. It contains a distillation and synthesis of material in the literature as well as some original results. The utility of the transformation theory is that it provides a means of obtaining Bethe-Salpeter amplitudes from the solutions of equations not of the Bethe-Salpeter variety. While applications of the theory are numerous, it is pointed out that the theory provides a means of placing phenomenological models in a field theoretical context, thereby eliminating one of the major objections to such models.;The second part of the dissertation introduces and solves a new phenomenological two fermion bound state model equation. The solutions of this equation are sixteen component spinors whose components are linear combinations of the so-called covariant harmonic oscillator wave functions. The mass squared eigenvalues of this equation are consistent with linearly rising Regge trajectories. The model is therefore presumed to describe mesons.;The third part presents some applications of the aforementioned model. In particular, a field theoretic expression for the transition matrix element describing the photodisintegration of the deuteron is taken from the literature and adapted to yield a similar expression describing meson photodecay. The formalism found in the literature is further extended in order to obtain the field theoretic two photon quark-antiquark annihilation amplitude. The bound state equation transformation theory is applied to both problems in order to obtain the transition matrix elements in terms of the solutions of the aforementioned phenomenological bound state equation.;Some discussion of theoretical details and suggestions for further work are found in an appendix.