A Gribov equation for the photon Green’s function

  • K. OdagiriEmail author
Regular Article - Theoretical Physics


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.


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Copyright information

© Springer-Verlag / Società Italiana di Fisica 2009

Authors and Affiliations

  1. 1.Condensed Matter Physics Group, Nanoelectronics Research InstituteNational Institute of Advanced Industrial Science and TechnologyTsukubaJapan

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