  The analytic continuation of the gluon propagator is revised in the light of
recent findings on the possible existence of complex conjugated poles. The
contribution of the anomalous pole must be added when Wick rotating, leading to
an effective Minkowskian propagator which is not given by the trivial analytic
continuation of the Euclidean function. The effective propagator has an
integral representation in terms of a spectral function which is naturally
related to a set of elementary (complex) eigenvalues of the Hamiltonian, thus
generalizing the usual K\"allen-Lehmann description. A simple toy model shows
how the elementary eigenvalues might be related to actual physical
quasiparticles of the non-perturbative vacuum.
