## Abstract

In this talk I will describe a series of calculations based on a general non-perturbative continuum approach to the problem of the IR behavior of QCO. This investigation, done in collaboration with F. Zachariasen and M. Baker, Is based on using the Schwinger-Dyson eqs. (hereafter S.D. eq.) for the quark and gluon propagators and using the appropriate Ward identities to obtain closed integral equations for the quantities of interest [1]. In particular, we have been able to show that a 1/q^{4} singularity in the gluon propagator produces a consistant solution to the integral equation. When this propagator is used in the integral equation for the quark propagator the pole singularity of a free massless quark is weakened to a simple square root branch point; furthermore we find that a mass-like tern (breaking chiral symmetry) which is an entire function, is consistent with the equations, though not required [2]. Finally, we construct an effective classical Lagrangian which is consistent with our form for the gluon propagator and automatically Includes the long range quantum fluctuations of QCD [3].

## Keywords

Entire Function Chiral Symmetry Ward Identity Vertex Function Gluon Propagator## Preview

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## References

- [1]M. Baker, J.S. Ball and F. Zachariasen, Nucl. Phys. B 186 (1981)531. M. Baker. J.S. Ball and F. Zachariasen, Nucl. Phys. B186 (1981) 560.CrossRefGoogle Scholar
- [2]J.S. Ball and F. Zachariasen. Phys. Letters 106B (1981) 133.Google Scholar
- [3]M. Baker and F. Zachariasen, Phys. Letters 108B (1982) 206.Google Scholar
- [4]See for example J.M. Cornwall, Phys. Rev. D22 (1980) 1452 and J.M. Cornwall, U.C.L.A. Preprint 81/TEP/8 (Feb. 1981).Google Scholar