  The non-perturbative structure of the photon and gluon propagators plays an
important role in governing the dynamics of quantum electrodynamics (QED) and
quantum chromodynamics (QCD) respectively. Although it is often assumed that
these interacting field propagators can be decomposed into longitudinal and
transverse components, as for the free case, it turns out that in general this
is not possible. Moreover, the non-abelian gauge symmetry of QCD permits the
momentum space gluon propagator to contain additional singular terms involving
derivatives of $\delta(p)$, the appearance of which is related to confinement.
Despite the possibility of the failure of the transverse-longitudinal
decomposition for the photon and gluon propagators, and the appearance of
singular terms in the gluon propagator, the Slavnov-Taylor identity
nevertheless remains preserved.
