  The Polyakov world-line path integral describing the propagation of gluon
field quanta is constructed by employing the background gauge fixing method and
is subsequently applied to analytically compute the divergent terms of the one
(gluonic) loop effective action to fourth order in perturbation theory. The
merits of the proposed approach is that, to a given order, it reduces to
performing two integrations, one over a set of Grassmann and one over a set of
Feynman-type parameters through which one manages to accomodate all Feynman
diagrams entering the computation at once.
