Aspects of scalar fields in gauge theories

Paterson, Andrew James (1980) Aspects of scalar fields in gauge theories. University of Southampton, Doctoral Thesis.

Abstract

This thesis is concerned with a variety of aspects of scalar fields ingauge theories: scalar Higgs particle production in a+e experiments, the scalar field effective potential, the Coleman-Weinberg phenomenon, phase transitions in gauge theories, and field theories of surfaces. First of all, situations are described in which production of the Higgs boson via bremsstrahlung from a virtual Zo is of interest. The cross-section for a+e + Z° + HZ° + HN+p is than calculated in detail and the results are compared with an independent, more general, analysis due to Jones and Petcov. It is concluded that there is the possibility of producing a light Higgs particle by exploiting its coupling to the Z° at energies in the range 60 GeV ti Ii < MZ. The remainder of the thesis is concerned with less phenomenological aspects of scalar fields. Chapter 3 reviews the calculation and some of the applications of the one loop approximation to the effective potential. Particular attention is given to the Gildener-Weinberg analysis of the Coleman-Weinberg phenomenon, as this topic is especially relevant to the work in the following chapter. In the fourth chapter, the chiral SU(n) x SU(n) linear a model is shown to possess no IR stable fixed points in d - 2 + e (e > 0) dimensions and to undergo a first order transition in four dimensions because of the Coleman-Weinberg phenomenon. The implications of this result on Migdal's approximate renormalisation group recursion relations are discussed. The final chapter briefly describes work in which scalar fields have been found to play an interesting role in the description of strings and generalised surfaces in gauge and non-gauge field theories.

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