The fate of the U(1) goldstone boson

Abstract

In the framework of a manifestly covariant formulation of (non-Abelian) gauge theories, we analyse what the gauge invariance (BRS invariance) implies for the problem of the Goldstone boson associated with the conserved U(1) axial vector current. Based on the symmetry consideration of gauge invariance only, it is shown that the Goldstone boson does not appear as a physical particle at all, if and only if the Faddeev-Popov (FP) ghost forms a massless bound state with the gauge boson in a pseudoscalar channel. This decoupling of the Goldstone boson from the physical sector is not caused by the Goldstone dipole proposed by Kogut and Susskind, but by a Goldstone quartet including the FP ghost bound state. This decoupling mechanism by the Goldstone quartet can be shown to become equivalent to that of the Goldstone dipole, only in a special case, i.e., the Schwinger model which is an Abelian theory in two dimensions. In the Abelian gauge theory in four dimensions, the chiral U(1) Goldstone boson necessarily appears as a physical particle.