Eur. Phys. J. C (2010) 65: 181-193
https://doi.org/10.1140/epjc/s10052-009-1188-7

Regular Article - Theoretical Physics

A Gribov equation for the photon Green’s function

Condensed Matter Physics Group, Nanoelectronics Research Institute, National Institute of Advanced Industrial Science and Technology, Tsukuba Central 2, 1-1-1 Umezono, Tsukuba, Ibaraki, 305-8568, Japan

^* e-mail: odagirik@gmail.com

Received: 9 May 2008
Revised: 24 September 2009
Published online: 10 November 2009

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 Trln 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, α _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 ∝ Q ² behavior for space-like Q ²=−q ². This implies the decoupling of the photon and an NJLVL-type effective theory in the UV limit.