Good ghosts are virtual particles that are introduced to maintain mathematical consistencies in a gauge theory; they often serve as a tool for regularization. A popular example is the
Faddeev–Popov ghosts, which arise in the quantization of
non-abelian gauge theories. These ghosts assist in the elimination of unphysical
degrees of freedom and preserve gauge invariance.
Faddeev–Popov ghosts Faddeev–Popov ghosts are extraneous
anticommuting fields that are introduced to maintain the consistency of the
path integral formulation in
non-abelian gauge theories, such as the ones describing
strong force. They are named after
Ludvig Faddeev and
Victor Popov.
Goldstone bosons Goldstone bosons are sometimes referred to as ghosts, mainly when speaking about the vanishing
bosons of the
spontaneous symmetry breaking of the
electroweak symmetry through the
Higgs mechanism. These
good ghosts are artifacts of gauge fixing. The longitudinal polarization components of the
W and Z bosons correspond to the Goldstone bosons of the spontaneously broken part of the electroweak symmetry
SU(2)⊗
U(1), which, however, are not observable. Because this symmetry is gauged, the three would-be Goldstone bosons, or ghosts, are "eaten" by the three
gauge bosons (
W± and
Z) corresponding to the three broken generators; this gives these three gauge bosons a mass, and the associated necessary third polarization degree of freedom. == Bad ghosts ==