DOI 10.1007/s100520000342
Gribov's equation for the Green function of light quarks
C. Ewerz1,2
1 Cavendish Laboratory, Cambridge University, Madingley Road, Cambridge
CB3 0HE, UK
2 DAMTP, Centre for Mathematical Sciences, Cambridge University,
Wilberforce Road, Cambridge CB3 0WA, UK
(e-mail: carlo@hep.phy.cam.ac.uk)
Received: 20 January 2000 / Published online: 6 March 2000 - © Springer-Verlag 2000
Abstract
Gribov's scenario of supercritical charges in QCD is investigated.
We perform a numerical study of the corresponding
equation for the Green function of light quarks. This is done
in an approximation which neglects all pion contributions.
Different types of solutions in the Euclidean region
are discussed and the mass function of the quark is calculated.
The solutions of the equation are shown to have a qualitatively
different behaviour if the strong coupling constant 
exceeds a critical value
in the infrared region.
Chiral symmetry breaking is found to occur
at supercritical coupling. The analytic structure of the solutions
is investigated. Earlier results obtained by Gribov are confirmed and
extended.
Copyright Società Italiana di Fisica, Springer-Verlag 2000
