# A Gribov equation for the photon Green's function

Source: [A Gribov equation for the photon Green's function](<https://www.sota2.com/research/paper/68fa295d1e209131ce833269>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-28T13:53:02.461Z

Authors: K. Odagiri

Published: 2008-05-09T16:51:27.000Z

## 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.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/0805.1382>)

[PDF](<https://arxiv.org/pdf/0805.1382.pdf>)