A Gribov equation for the photon Green's function
Abstract
We present a derivation of the Gribov equation for the gluon/photon Green's function D(q). Our derivation is based on the second derivative of the gauge-invariant quantity Tr ln D(q), which we interpret as the gauge-boson `self-loop'. By considering the higher-order corrections to this quantity, we are able to obtain a Gribov equation which sums the logarithmically enhanced corrections. By solving this equation, we obtain the non-perturbative running coupling in both QCD and QED. In the case of QCD, alpha_S has a singularity in the space-like region corresponding to super-criticality, which is argued to be resolved in Gribov's light-quark confinement scenario. For the QED coupling in the UV limit, we obtain a \propto Q^2 behaviour for space-like Q^2=-q^2. This implies the decoupling of the photon and an NJLVL-type effective theory in the UV limit.
Keywords
Cite
@article{arxiv.0805.1382,
title = {A Gribov equation for the photon Green's function},
author = {K. Odagiri},
journal= {arXiv preprint arXiv:0805.1382},
year = {2010}
}
Comments
12 pages, 5 figures; version to be published in Eur. Phys. J. C