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An Extended Perturbation Theory for QCD

  • M. Stingl

Abstract

An outline is given of a systematic, extended iterative solution to the Euclidean Dyson-Schwinger equations of QCD. While still assuming the possibility of a semi-convergent expansion in powers of [g(v 0)/4π]2 at all scales v 0, it admits in the coefficients a rational dependence on the prototype quantity non-analytic in g(v 0), the spontaneous QCD mass scale A. Self-consistency of nonperturbatively modified, zeroth-order, proper vertices in the DS equations occurs through a mechanism of „nonperturbative logarithms“, which is tied to the presence of divergences in DS loop integrals, and thus represents a pure quantum effect similar to anomalies. An interesting aspect of the scheme is the existence of solutions in which the basic gluon and quark propagators have no stable-particle poles, and describe short-lived elementary excitations, leading to a weak-coupling description of confinement.

Keywords

Invariant Function Elementary Excitation Loop Integral Quark Propagator Basic Vertex 
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References

  1. Ahlbach, J., Lavelle, M.J. and Schaden, M., 1992, Phys. Lett. B275: 124Google Scholar
  2. Baker, G.A., Jr., and Gammel, J.L., The Pade’ Approximant in Theoretical Physics, Academic Press, New York, (1970)Google Scholar
  3. Becker, M., Löffler, G., Pesch, A., Stingl, M. and Rosenfelder, R., 1991, Phys. Lett. B267: 261Google Scholar
  4. Callan, C.G., Dashen, R.F., and Gross, D.J., 1978, Phys. Rev. D17:2717 Eichten, E.J. and Feinberg, F.L., 1974, Phys. Rev. D10: 3254Google Scholar
  5. Gross, D.J. and Neveu, A., 1974, Phys. Rev. D10: 3235ADSGoogle Scholar
  6. Häbel, U., Könning, R., Reusch, H.G., Stingl, M. and Wigard, S., 1990, Z. Physik A336:423 and 435Google Scholar
  7. Könning, R., 1990, Dr. rer. nat. thesis, University of Münster (in German) Lavelle, M.J., and Oleszczuk, 1991, M., Z. Physik C51: 615Google Scholar
  8. Lavelle, M.J., 1992, contribution to this volumeGoogle Scholar
  9. Lehmann, H., 1954, Nuovo Cim. 11: 342MATHCrossRefGoogle Scholar
  10. Marciano, W. and Pagels, H., 1978, Phys. Reports 36C:137 Polkinghorne, J.C., 1975, Nucl. Phys. B93: 515Google Scholar
  11. Preparata, G., 1973, Phys. Rev. D7: 2973ADSGoogle Scholar
  12. Schwinger, J., 1962, Phys. Rev. 125 397MathSciNetADSMATHCrossRefGoogle Scholar
  13. Stingl, M., 1986, Phys. Rev. D34:3863, Erratum ibid. D36: 651 (1987)Google Scholar

Copyright information

© Springer Science+Business Media New York 1994

Authors and Affiliations

  • M. Stingl
    • 1
  1. 1.University of MünsterMünsterGermany

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