The European Physical Journal C

, Volume 1, Issue 1–2, pp 343–350 | Cite as

(Anti-)self-dual homogeneous vacuum gluon field as an origin of confinement and SUL(NF) × SUR(NF) symmetry breaking in QCD

  • G. V. Efimov
  • S. N. Nedelko


It is shown that an (anti-) self-dual homogeneous vacuum gluon field appears in a natural way within the problem of calculation of the QCD partition function in the form of Euclidean functional integral with periodic boundary conditions. There is no violation of cluster property within this formulation, nor are parity, color and rotational symmetries broken explicitly. The massless limit of the product of the quark masses and condensates,\(m_f \left\langle {\bar \psi _f \psi _f } \right\rangle \), is calculated to all loop orders. This quantity does not vanish and is proportional to the gluon condensate appearing due to the nonzero strength of the vacuum gluon field. We conclude that the gluon condensate can be considered as an order parameter both for confinement and chiral symmetry breaking.


Partition Function Zero Mode Chiral Symmetry Breaking Background Field Homogeneous Field 
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  1. 1.
    H. Leutwyler: Phys. Lett.96B (1980) 154ADSCrossRefMathSciNetGoogle Scholar
  2. 2.
    H. Leutwyler: Nucl. Phys.B179 (1981) 129ADSCrossRefGoogle Scholar
  3. 3.
    E. Elizalde: Nucl. Phys.B243 (1984) 398;ADSCrossRefGoogle Scholar
  4. 3a.
    E. Elizalde, J. Soto:ibid,B260 (1985) 136ADSCrossRefMathSciNetGoogle Scholar
  5. 4.
    H. Pagels, E. Tomboulis: Nucl. Phys.B143 (1978) 485ADSCrossRefMathSciNetGoogle Scholar
  6. 5.
    G.V. Efimov, S.N. Nedelko: Phys. Rev.D51 (1995) 174ADSGoogle Scholar
  7. 6.
    Ja.V. Burdanov, G.V. Efimov, S.N. Nedelko, S.A. Solunin: Phys. Rev.D54 (1996) 4483ADSGoogle Scholar
  8. 7.
    D. Dineykhan, G.V. Efimov, G. Ganbold, S.N. Nedelko: “Oscillator Representation in Quantum Physics”, LNP series “monographs”, m26 (Springer-Verlag, Heidelberg, 1995);Google Scholar
  9. 7a.
    S.V. Abramova, G.V. Efimov, S.N. Nedelko: Phys.Rev.D52 (1995) 6098ADSGoogle Scholar
  10. 8.
    B.S. DeWitt: Phys. Rev.162 (1967) 1195, 1239ADSCrossRefzbMATHGoogle Scholar
  11. 9.
    L.F. Abbott: Nucl. Phys.B185 (1981) 189ADSCrossRefGoogle Scholar
  12. 10.
    P. Minkowski: Nucl. Phys.B177 (1981) 203ADSCrossRefGoogle Scholar
  13. 11.
    H.D. Trottier, and R.M. Woloshyn: Phys. Rev. Lett.70 (1993) 2053ADSCrossRefGoogle Scholar
  14. 12.
    S. Coleman: in Proceedings of the 1977 International School of Subnuclear Physics, Erice, Italy (Plenum Press, New York, 1979)Google Scholar
  15. 13.
    R. Carlitz, D.B. Creamer: Ann. Phys. (NY)118 (1979) 429;ADSCrossRefGoogle Scholar
  16. 13a.
    A.V. Smilga: Phys. Rev.D49 (1994) 6836ADSGoogle Scholar
  17. 14.
    C.A. Flory: Phys. Rev.D28 (1984) 1425ADSGoogle Scholar
  18. 15.
    L.S. Brown, R.D. Carlitz, D.B. Creamer, C. Lee: Phys. Rev.D17 (1978) 1583ADSGoogle Scholar
  19. 16.
    L.S. Brown, R.D. Carlitz, C. Lee: Phys. Rev.D16 (1977) 417;ADSGoogle Scholar
  20. 16a.
    L.S. Brown, C. Lee: Phys. Rev.D18 (1978) 2180ADSGoogle Scholar
  21. 17.
    G. V. Efimov, M. A. Ivanov: “The Quark Confinement Model of Hadrons” (IOP Publishing, Bristol and Philadelphia, 1993)Google Scholar
  22. 18.
    G. V. Efimov: “Nonlocal interactions of quantized fields” (Nauka, Moscow, 1977);Google Scholar
  23. 18a.
    G.V. Efimov, V.A. Alebastrov: Comm. Math. Phys.31 (1973) 1;ADSCrossRefzbMATHMathSciNetGoogle Scholar
  24. 18b.
    G.V. Efimov, O.A. Mogilevsky, Nucl.Phys.B44 (1972) 541ADSCrossRefGoogle Scholar

Copyright information

© Springer-Verlag 1998

Authors and Affiliations

  • G. V. Efimov
    • 1
  • S. N. Nedelko
    • 1
    • 2
  1. 1.Bogoliubov Laboratory of Theoretical PhysicsJoint Institute for Nuclear ResearchDubna, Moscow RegionRussia
  2. 2.Institute for Theoretical PhysicsUniversity of Erlangen-NürnbergErlangenGermany

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