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In order to construct a gauge invariant two-point function in a Yang-Millstheory, we propose the use of the all-order gauge invariant transverseconfigurations A^h. Such configurations can be obtained through theminimization of the functional A^2_{min} along the gauge orbit within the BRSTinvariant formulation of the Gribov-Zwanziger framework recently put forward in[1,2] for the class of the linear covariant gauges. This correlator turns outto provide a characterization of non-perturbative aspects of the theory in aBRST invariant and gauge parameter independent way. In particular, it turns outthat the poles of <A^h A^h> are the same as those of the transverse part of thegluon propagator, which are also formally shown to be independent of the gaugeparameter entering the gauge condition through the Nielsen identities. Thelatter follow from the new exact BRST invariant formulation introduced before.Moreover, the correlator <A^h A^h> enables us to attach a BRST invariantmeaning to the possible positivity violation of the corresponding temporalSchwinger correlator, giving thus for the first time a consistent, gaugeparameter independent, setup to adopt the positivity violation of <A^h A^h> asa signature for gluon confinement. Finally, in the context of gauge theoriessupplemented with a fundamental Higgs field, we use <A^h A^h> to probe the polestructure of the massive gauge boson in a gauge invariant fashion.

physical review. d/physical review. d.

Non-perturbative aspects of Euclidean Yang-Mills theories in linear  covariant gauges: Nielsen identities and a BRST invariant two-point  correlation function