Abstract
We introduce, within the refined Gribov-Zwanziger setup, a composite Becchi-Rouet-Stora-Tyutin (BRST) invariant fermionic operator coupled to the inverse of the Faddeev-Popov operator. As a result, an effective BRST invariant action in Euclidean space-time is constructed, enabling us to pave the first step towards the study of the behavior of the fermion propagator in the infrared region in the class of the linear covariant gauges. The aforementioned action is proven to be renormalizable to all orders by means of the algebraic renormalization procedure.
Highlights
Despite the nontrivial progress done in the last decades, see [1] for a general overview, a satisfactory solution of the Gribov problem [2] is still lacking
Within the refined Gribov-Zwanziger setup, a composite Becchi-Rouet-Stora-Tyutin (BRST) invariant fermionic operator coupled to the inverse of the Faddeev-Popov operator
An effective BRST invariant action in Euclidean space-time is constructed, enabling us to pave the first step towards the study of the behavior of the fermion propagator in the infrared region in the class of the linear covariant gauges
Summary
We shall introduce a unique generalized BRST operator encoding all three operators ðs; δ; δÞ. Let us end this section by presenting the explicit expression of the complete tree-level starting action Σ of Eq (77): 4The parameters ðα; χÞ do not transform under ðδ; δÞ, δα 1⁄4 δχ 1⁄4 δα 1⁄4 δχ 1⁄4 0: ð78Þ. It is helpful here to provide the mass dimensions and the other quantum numbers of all fields and sources appearing in the complete action Σ. These quantum numbers are displayed in the tables below (up to Table V), where the commuting (C) or anticommuting (A) nature of each variable is shown, being determined as the sum of the ghost charges and of the so-called e-charge (i.e., the spinor index). When this sum is even, the corresponding field/source is considered a commuting variable, otherwise it is an anticommuting one
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