Quark and gluon propagators in quantum chromodynamics

Abstract

The quark and gluon propagators of massless quantum chromodynamics are studied in the Landau gauge using renormalization-group techniques in combination with the analytic properties which follow from Lorentz invariance and spectrum conditions. The investigations include the possibility of a spontaneous breakdown of global color symmetry with mass generation for quarks and gluons. The explicit asymptotic behavior of the propagators for large momenta is determined along all directions in the cut complex plane. It is found that the propagators cannot be entire functions except possibly in the infrared-stable limit. The existence of branch cuts drawn to infinity is verified. Projected propagators are introduced where contributions from negative-norm states are omitted. The original as well as the projected propagators satisfy unsubtracted spectral representations. The positivity condition of the transverse projected weight function leads to a restriction for the anomalous dimension of the gluon field, which implies a lower bound for the number of flavors.