Some studies on the consequences of internal symmetry and supergauge invariance in particle physics

Abstract

The object of this thesis is twofold. The first part concerns the improvement of the unitary operator of Buccella et al. This operator is an example of a Melosh transformation connecting the algebras of the constituent and current quarks. The second part of this thesis examines the structure of the multiplets and the corresponding Lagrangians arising from the enlarged supersymmetry algebra incorporating isospin. Chapter One is a general introduction to the Melosh transformation and the work done by Buccella et al. The second chapter examines the difficulties involved with the Buccella transformation and contains a discussion on its possible improvement. In the third and final chapter on the Buccella transformation these improvements are implemented successfully, giving a unitary transformation which is correct to the second order of a perturbation expansion. Using this transformation we are able to obtain mass equations which are in good agreement with experiment in addition to the usual successful predictions for axial couplings typical of Melosh transformations in general. Chapter Four gives a general introduction to the concept of supersymmetry, describing the successes of the original model and also its special points of interest. The fifth chapter looks in detail at the structure of the multiplets arising from the larger super-algebra incorporating isospin, suggested by Salam and Strathdee. In the sixth chapter we try to form "super-invariant" Lagrangian densities from these multiplets which are physically applicable. Finally there is a discussion of our conclusions.