Gauge-invariance properties and singularity cancellations in a modified PQCD

  • A. CaboEmail author
  • M. Rigol
Theoretical Physics


The gauge-invariance properties and singularity elimination of the modified perturbation theory for QCD introduced in previous works are investigated. The construction of the modified free propagators is generalized to include the dependence on the gauge parameter α. Further, a functional proof of the independence of the theory under the changes of the quantum and classical gauges is given. The singularities appearing in the perturbative expansion are eliminated by properly combining dimensional regularization with the Nakanishi infrared regularization for the invariant functions in the operator quantization of the α-dependent gauge theory. First-order evaluations of various quantities are presented, illustrating the gauge-invariance properties.


Ghost Singular Term Dimensional Regularization Gauge Parameter Gluon Propagator 
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  1. 1.
    T. Schäfer, E.V. Shuryak, Rev. Mod. Phys. 70, 323 (1998)CrossRefADSGoogle Scholar
  2. 2.
    A. Cabo, S. Peñaranda, R. Martinez, Mod. Phys. Lett. A 10, 2413 (1995)CrossRefADSGoogle Scholar
  3. 3.
    M. Rigol, A. Cabo, Phys. Rev. D 62, 074018 (2000) [hep-th/9909057]CrossRefADSGoogle Scholar
  4. 4.
    A. Cabo, M. Rigol, Eur. Phys. J. C 23, 289 (2002) [hep-ph/0008003]CrossRefADSGoogle Scholar
  5. 5.
    M. Rigol, About an alternative vacuum state for perturbative QCD, Graduate Dissertation Thesis, Instituto Superior de Ciencias y Tecnología Nucleares, La Habana, Cuba, 1999Google Scholar
  6. 6.
    A. Cabo, JHEP 04, 044 (2003) [hep-ph/0209215(2002)]CrossRefADSGoogle Scholar
  7. 7.
    G.K. Savvidy, Phys. Lett. B 71, 133 (1977)CrossRefADSGoogle Scholar
  8. 8.
    I.A. Batalin, S.G. Matinyan, G.K. Savvidy, Sov. J. Nucl. Phys. 26, 214 (1977)Google Scholar
  9. 9.
    A. Cabo, O.K. Kalashnikov, A.E. Shabad, Nucl. Phys. B 185, 473 (1981)CrossRefADSGoogle Scholar
  10. 10.
    W. Dittrich, M. Reuter, Phys. Lett. B 128, 321 (1983)CrossRefADSGoogle Scholar
  11. 11.
    P. Hoyer, HIP-2002-44-TH, September 2002. 3pp.; Talk given at 31st International Conference on High Energy Physics, ICHEP 367-369, Amsterdam (2002) [hep-ph/0209318]Google Scholar
  12. 12.
    M.A. Shifman, A.I. Vainshtein, V.I. Zakharov, Nucl. Phys. B 147, 385, 448, 519 (1979)CrossRefADSGoogle Scholar
  13. 13.
    R. Fukuda, Phys. Rev. D 21, 485 (1980)MathSciNetCrossRefADSGoogle Scholar
  14. 14.
    K.G. Chetyrkin, S. Narison, V.I. Zakharov, Nucl. Phys. B 550, 353 (1999)CrossRefADSGoogle Scholar
  15. 15.
    S.J. Huber, M. Reuter, M.G. Schmidt, Phys. Lett. B 462, 158 (1999)CrossRefADSGoogle Scholar
  16. 16.
    P. Hoyer, NORDITA – 96/63 P (1996), hep-ph/9610270 (1996); P. Hoyer, NORDITA – 97/44 P (1997), hep-ph/9709444 (1997)Google Scholar
  17. 17.
    H.J. Munczek, A.M. Nemirovsky, Phys. Rev. D 55, 3455 (1983)Google Scholar
  18. 18.
    C.J. Burden, C.D. Roberts, A.G. Williams, Phys. Lett. B 285, 347 (1992)CrossRefADSGoogle Scholar
  19. 19.
    T. Kugo, I. Ojima, Prog. Theor. Phys. Suppl. 66, 1 (1979)MathSciNetGoogle Scholar
  20. 20.
    N. Nakanishi, I. Ojima, Covariant operator formalism of gauge theories and quantum gravity, (Singapore, Word Scientific, 1990)Google Scholar
  21. 21.
    H.P. Pavel, D. Blaschke, V.N. Pervushin, G. Röpke, Int. J. Mod. Phys. A 14, 205 (1999)MathSciNetCrossRefADSGoogle Scholar
  22. 22.
    N. Nakanishi, Prog. Theor. Phys. 51, 952 (1974); N. Nakanishi, Prog. Theor. Phys. 52, 1929 (1974)CrossRefADSGoogle Scholar
  23. 23.
    D.G. Boulware, Phys. Rev. D 23, 389 (1981)MathSciNetCrossRefADSGoogle Scholar
  24. 24.
    B.S. DeWitt, in Proceedings: Symposium on Quantum Gravity II, eds. C. Isham, R. Penrose, D. Sciama, (Clarendon Press, Oxford, 1981)Google Scholar
  25. 25.
    G. ’t Hooft, in 12th Winter School of Theoretical Physics Functional and Probabilistic Methods in Quantum Field Theory, Karpacz, Poland, 17 February–2 March 1975, Acta Universitatis Wratislaviensis No. 368, eds. J. Lopuszánski, B. Jancewicz, Vol. 1, 1976Google Scholar
  26. 26.
    G. Leibbrandt, Rev. Mod. Phys. 47, 849 (1975)MathSciNetCrossRefADSGoogle Scholar
  27. 27.
    T. Muta, Foundations of Quantum Chromodynamics, World Scientific Lectures Notes in Physics – Vol. 5, 1987Google Scholar
  28. 28.
    S. Gasiorowicz, Elementary particle physics (John Wiley, New York, 1966)Google Scholar
  29. 29.
    L.D. Faddeev, A.A. Slanov, Gauge fields. Introduction to quantum theory (Benjamin Cummings Publishing, 1980)Google Scholar
  30. 30.
    B. Sakita, Quantum Theory of Many Variable Systems and Fields, World Scientific Lecture Notes in Physics, Vol. 1, 1985Google Scholar
  31. 31.
    J. Zinn-Justin, in Trends in Elementary Particle Theory, Lecture Notes in Physics, Vol. 37, Springer, 1975Google Scholar
  32. 32.
    S. Coleman, E. Weinberg, Phys. Rev. D 7, 1888 (1973)CrossRefADSGoogle Scholar
  33. 33.
    A. Cabo, D. Martinez-Pedrera, ICTP Preprint IC/2004/ 118 (2004), hep-ph/0501054(2005); to appear in Eur. Phys. J. CGoogle Scholar

Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  1. 1.Theory DivisionCERNGenevaSwitzerland
  2. 2.Group of Theoretical PhysicsInstituto de Cibernética, Matemática y Físicala HabanaCuba
  3. 3.Physics DepartmentUniversity of CaliforniaDavisUSA

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