General Methods for Analyzing Higgs Potentials

Author: Kim, Jai Sam

Year: 1982

Degree: Dissertation (Ph.D.)

Advisor: Gell-Mann, Murray

Committee Members: Gell-Mann, Murray; Frautschi, Steven C.; Pine, Jerome; Koonin, Steven E.

Option: Physics

DOI: 10.7907/RAFF-A683

Abstract

This thesis is based on several papers published by the author and some more work to be published. We explain the technical problem of minimizing Higgs potentials using group theoretical concepts. Three mathematical results which belong to distinct areas are used to analyze the Higgs potential in an abstract way. The problem reduces to one of finding "contours" of directional minima and thus our method is geometrical. It is explained in detail and demonstrated for some simple cases. We show that the Michel-Radicati conjecture and the Gell-Mann-Slansky conjecture have geometrical significance besides predicting the most likely symmetry groups of the absolute minimum of the potential. We also apply the method to a non-monotonic potential.

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