Mass Generation via the Phase Transition of the Higgs Field.

The commonly quoted bistable Higgs potential is not a proper description of the Higgs field because, among other technical reasons, one of its stable states acquires a negative expectation value in vacuum. We rely on formal catastrophe theory to derive the form of the Higgs potential that admits only one positive mean value in vacuum. No symmetry is broken during the ensuing phase transition that assigns mass to the Higgs field; only gauge redundancy is "broken" by the appearance of phase in the massive state, but this redundancy is not a true symmetry of the massless field. Furthermore, a secondary, certainly amusing conclusion, is that, in its high-energy state, the field oscillates about its potential minimum between positive and negative masses, but it is doubtful that such evanescent states can survive below the critical temperature of 159.5 GeV, where the known particles were actually created. [ABSTRACT FROM AUTHOR]