Some Remarks on the Higgs Mechanism

Abstract

AbstractWe show that at least one of the auxiliary one‐component fields in the Higgs Model – the field ϕ – is not a Lorentz scalar and that it is probably not local with respect to the current. Our conclusion is that we cannot prescribe to the field ϕ a direct physical meaning.In case ϕ is not local with respect to the current it is likely that the zero eigenvalue of the mass operator does not appear in the theory at all.In case ϕ is quasilocal with respect to j0, such an eigenvalue appears at least in the original Model and the mass spectrum can be different for different versions of the Model. We conjecture that this can be explained with help of the theory of unitarily inequivalent representations.We display the difficulty in translating into the quantal language the classical procedure leading from the original Model to the variant of unitary gauge. We hope that with help of unitarily inequivalent representations this difficulty can be resolved.We exhibit the fact that in the Higgs Model the whole gauge group does not have a direct physical meaning, in contradistinction to electrodynamics, where the local gauge group only has no physical significance.