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The gauge-invariant generation of a dynamical, momentum-dependent gluon massis intimately connected with the presence of non-perturbative massless poles inthe vertices of the theory, which trigger the well-known Schwinger mechanism.In the deep infrared the integral equation that governs this effective gluonmass assumes a particularly simple form, which may be derived following twoseemingly different, but ultimately equivalent procedures. In particular, itmay be obtained either as a deviation from a special identity that enforces themasslessness of the gluon in the absence of massless poles, or as a directconsequence of the appearance of a non-vanishing bound-state wave function,associated with the details of the actual formation of these massless poles. Inthis presentation we demonstrate that, due to profound relations between thevarious ingredients, the two versions of the gluon mass equation are in factabsolutely identical.

Infrared properties of the gluon mass equation