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The structure of the quark propagator of $QCD$ in a confining background isnot known. We make an Ansatz for it, as hinted by a particular mechanism forconfinement, and analyze its implications in the meson and baryon correlators.We connect the various terms in the K\"allen-Lehmann representation of thequark propagator with appropriate combinations of hadron correlators, which mayultimately be calculated in lattice $QCD$. Furthermore, using the positivity ofthe path integral measure for vector like theories, we reanalyze some massinequalities in our formalism. A curiosity of the analysis is that, the exoticcomponents of the propagator (axial and tensor), produce terms in the hadroncorrelators which, if not vanishing in the gauge field integration, lead toviolations of fundamental symmetries. The non observation of these violationsimplies restrictions in the space-time structure of the contributing gaugefield configurations. In this way, lattice $QCD$ can help us analyze themicroscopic structure of the mechanisms for confinement.Comment: 12 pp in LaTeX, preprint Univ. of Valencia, FTUV/94-16, IFIC/94-15.  To appear in Z.Phys.

Hadron correlators and the structure of the quark propagator