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In QCD both the quark and ghost propagators are important for governing thenon-perturbative dynamics of the theory. It turns out that the dynamicalproperties of the quark and ghost fields impose non-perturbative constraints onthe analytic structure of these propagators. In this work we explicitly derivethese constraints. In doing so we establish that the corresponding spectraldensities include components which are multiples of discrete mass terms, andthat the propagators are permitted to contain singular contributions involvingderivatives of $\delta(p)$, both of which are particularly relevant in thecontext of confinement.

Non-perturbative constraints on the quark and ghost propagators