Dipole-Ghost Goldstone Bosons in the Higgs Model and in the Schwinger Model

Abstract

The Higgs model is analyzed in the framework of indefinite-metric quantum field theory. It is shown that Goldstone bosons become dipole ghosts in 'the linear covariant gauges other than· the Landau gauge. It is also shown in the covariaJ:J.t-gauge formalism that the Schwinger model (the two-dimensional massless quantum electrodynamics) is quite analogous to the Higgs model as far as Goldstone bosons are concerned. § I. Introduction In previous work/l-sl the present author clarified why and how the Higgs mechanism (Higgs phenomenon)•> is compatible with the Goldstone theorem 5> in the framework of local quantum field theory. The formalism developed there was based on manifestly covariant quantum electrodynamics involving a gauge parameter a.6> Particular attention was paid to the Landau-gauge case (a=O) because of having the Lorentz condition 8# At He has thereby found that spontaneous breakdown of symmetry does occur in the Schwinger model, contrary to the assertion of Kog11t and Suss­ kind.9> Thus the so-called Schwinger mechanism is shown to be a special case of the Higgs mechanism. In the present paper, we ext~nd Ito's analysis t~ the a=FO case (§ 3). We then find that there is complete parallelism between the Schwinger model and the Higgs model as far as Goldstone bosons . are concerned.