Abstract
In this paper, a proposal for the restriction of the Euclidean functional integral to a region free from infinitesimal Gribov copies in linear covariant gauges is discussed. An effective action, akin to the Gribov–Zwanziger action of the Landau gauge, is obtained which implements the aforementioned restriction. Although originally non-local, this action can be cast in local form by introducing auxiliary fields. As in the case of the Landau gauge, dimension two condensates are generated at the quantum level, giving rise to a refinement of the action which is employed to obtain the tree-level gluon propagator in linear covariant gauges. A comparison of our results with those available from numerical lattice simulations is also provided.
Highlights
Analytical approaches to quantum chromodynamics (QCD) face many problems due to the fact that at low energy scales, where many important physical phenomena as confinement and chiral symmetry breaking take place, perturbation theory breaks down
Motivated by the previous Theorem, we introduce the following Gribov region LCG in the linear covariant gauges: Definition 2.1 The Gribov region LCG in linear covariant gauges is given by LCG = Aaμ, ∂μ Aaμ − αba = 0, MT ab > 0, (22)
The understanding of the Gribov issue in the linear covariant gauges cannot certainly be compared to that achieved in the Landau gauge, the possibility of introducing the region LCG which is free from infinitesimal copies can be regarded a first important step in order to face this highly non-trivial problem
Summary
Analytical approaches to quantum chromodynamics (QCD) face many problems due to the fact that at low energy scales, where many important physical phenomena as confinement and chiral symmetry breaking take place, perturbation theory breaks down. Page 3 of 12 479 that, besides the Landau and maximal Abelian gauges, a successful characterization of the Gribov region and of the ensuing GZ and RGZ actions has been worked out in the non-covariant Coulomb gauge [20,21,22,23,24] All these three gauges share the very important feature that the corresponding Faddeev–Popov operators are Hermitian. Unlike the Landau, Coulomb, and maximal Abelian gauges, the Faddeev–Popov operator lacks hermiticity and, no auxiliary functional is at our disposal, making the treatment of the Gribov copies highly non-trivial Despite these difficulties, a first attempt to address the Gribov problem in the linear covariant gauges was discussed in [25], under the assumptions that the gauge parameter α present in these gauges was considered to be infinitesimal, i.e. α 1.
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