Dynamical Quark Mass Generation in QCD\textsubscript{3} within the Hamiltonian approach in Coulomb gauge

Abstract

We investigate the equal-time (static) quark propagator in Coulomb gauge within the Hamiltonian approach to QCD in \(d=2\) spatial dimensions. Although the underlying Clifford algebra is very different from its counterpart in \(d=3\), the gap equation for the dynamical mass function has the same form. The additional vector kernel which was introduced in \(d=3\) to cancel the linear divergence of the gap equation and to preserve multiplicative renormalizability of the quark propagator makes the gap equation free of divergences also in \(d=2\).