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A Gribov equation for the photon Green’s function

  • K. OdagiriEmail author
Regular Article - Theoretical Physics

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.

PACS

11.10.Lm 11.15.Ex 11.15.Tk 12.38.Aw 

References

  1. 1.
    V.N. Gribov, Eur. Phys. J. C 10, 71 (1999). arXiv:hep-ph/9807224 MathSciNetADSGoogle Scholar
  2. 2.
    V.N. Gribov, Eur. Phys. J. C 10, 91 (1999). arXiv:hep-ph/9902279 ADSGoogle Scholar
  3. 3.
    Yu.L. Dokshitzer, D.E. Kharzeev, arXiv:hep-ph/0404216
  4. 4.
    V.N. Gribov, Orsay lectures on confinement. arXiv:hep-ph/9403218, arXiv:hep-ph/9407269, arXiv:hep-ph/9905285
  5. 5.
    V.N. Gribov, Quantum electrodynamics at short distances (1996, unpublished) Google Scholar
  6. 6.
    V.N. Gribov, Gauge Theories and Quark Confinement (Phasis Publishing House, Moscow, 2002). pp. 519–554. Collection of works Google Scholar
  7. 7.
    V.N. Gribov, Phys. Lett. B 336, 243 (1994). arXiv:hep-ph/9407269 CrossRefADSGoogle Scholar
  8. 8.
    Y. Nambu, G. Jona-Lasinio, Phys. Rev. 122, 345 (1961) CrossRefADSGoogle Scholar
  9. 9.
    V.G. Vaks, A.I. Larkin, Zh. Eksp. Teor. Fiz. 40, 282 (1961) Google Scholar
  10. 10.
    V.G. Vaks, A.I. Larkin, Sov. Phys. JETP 13, 192 (1961) zbMATHGoogle Scholar
  11. 11.
    J.M. Luttinger, J.C. Ward, Phys. Rev. 118, 1417 (1960) zbMATHCrossRefMathSciNetADSGoogle Scholar
  12. 12.
    A.A. Abrikosov, L.P. Gorkov, I.E. Dzyaloshinski, Methods of Quantum Field Theory in Statistical Physics (Dover, New York, 1963). See Sect. 19.4 zbMATHGoogle Scholar
  13. 13.
    W.E. Caswell, Phys. Rev. Lett. 33, 244 (1974) CrossRefADSGoogle Scholar
  14. 14.
    R.K. Ellis, W.J. Stirling, B.R. Webber, Camb. Monogr. Part. Phys. Nucl. Phys. Cosmol. 8, 1 (1996) Google Scholar
  15. 15.
    O.V. Tarasov, A.A. Vladimirov, A.Y. Zharkov, Phys. Lett. B 93, 429 (1980) CrossRefADSGoogle Scholar
  16. 16.
    S.A. Larin, J.A.M. Vermaseren, Phys. Lett. B 303, 334 (1993). arXiv:hep-ph/9302208 CrossRefADSGoogle Scholar
  17. 17.
    T. van Ritbergen, J.A.M. Vermaseren, S.A. Larin, Phys. Lett. B 400, 379 (1997). arXiv:hep-ph/9701390 CrossRefADSGoogle Scholar
  18. 18.
    G. Cvetič, Rev. Mod. Phys. 71, 513 (1999). arXiv:hep-ph/9702381 CrossRefADSGoogle Scholar
  19. 19.
    J.B. Kogut, E. Dagotto, A. Kocic, Phys. Rev. Lett. 60, 772 (1988) CrossRefADSGoogle Scholar
  20. 20.
    K. Odagiri, work in progress. See arXiv:0903.2125 [hep-th], which is currently under major revision

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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