The Schwinger-Dyson equations and confinement in quantum chromo-dynamics

The thesis presents Schwinger-Dyson equations and confinement in quantum chromodynamics. The Schwinger-Dyson equations for the gluon and quark propagators are investigated in the covariant gauge. The renormalization functions are approximated suitably and the value of the parameters are determined by requiring that the functions be numerically self-consistent solutions over appropriate ranges of momemta. In the case of the gluon, the Schwinger-Dyson equation is truncated by neglecting the two loop contributions and the triple gluon vertex is approximated. In the quark case the dominant part of quark-gluon vertex is determined from the Ward-Takahashi identity to give, with the gluon, a closed equation. It is found that the gluon propagator has approximately a singularity of the form 1/q4 which leads to a roughly linear confining potential. The effect of this enhanced singularity on the quark propagator is to suppress the propagation of quarks at low momemta. (U.K.)