On Classical Configurations of SU(2) Gauge-Higgs System

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Abstract
Two classical static configurations of the SU (2) gauge-Higgs system are known: the sphaleron and the string-monopole configuration. In addition, a third configuration, new sphaleron, has been conjectured to exist. A series of field configurations at spatial infinity is examined, such that the ansatz for the sphaleron and that for the string-monopole configuration are given by the n = 2 and n = 1 sectors of the series respectively and the n = 4 sector is the ansatz for the new sphaleron. A specific gauge transformation, which is singular and relates the Dirac and the 't Hooft-Polyakov monopoles, and Hopf projection map, which induces noncontractable structure in field configuration space, are investigated to produce the series. It is conjectured that the SU (2) gauge-Higgs system might admit more classical configurations. A peculiar property of the sphaleron that, in spite of sitting at a saddle point of energy, it enjoys maximal symmetry of the gauge-Higgs system is discussed.

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