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UBC Theses and Dissertations

Numerical analysis of a unitary particle model. Kennedy, Edith Mary

Abstract

This thesis investigates a classical unitary field model consisting of a complex scalar source field coupled to a real scalar massless field, in an attempt to describe the family of heavy particles consisting of nucleons and hyperons. The discussion is limited to spherically symmetric fields and approximate methods are used to solve the non-linear field equations. The solutions may be classified by the number of nodes in the source field. For each type of solution, the energy in the field is calculated as a function of the spatial extension of the particle described by that solution. A striking feature of the theory is that for each type of solution the energy may be minimized with respect to the extension of the particle. The particular solution which yields the minimum energy is interpreted as representing a particle in its normal state. In this way, a discrete mass spectrum is obtained. The mass ratios yielded by the theory compare reasonably well with the experimentally observed mass ratios for nucleons, ⋀ particles and Σ particles. A comparison of theoretical and experimental values determines the "bare" mass of the source field to correspond to 1185 electron masses, and yields a value for the ratio of the normalization constant of the source field to the coupling constant of the two fields, but does not specify these latter constants separately. Limitations of this classical model are stated. A possible improvement of the model is investigated in an attempt to improve the theoretical mass ratios; however, the significant features of the model remain unchanged, and the change in the mass ratios, while in the right direction, is very slight.

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