Confining solution of the Dyson-Schwinger equations in Coulomb gauge

The Dyson-Schwinger equations arising from minimizing the vacuum energy density in the Hamiltonian approach to Yang-Mills theory in Coulomb gauge are solved numerically. A new solution is presented which gives rise to a strictly linearly rising static quark potential and whose existence was previously observed in the infrared analysis of the Dyson-Schwinger equations. For the new solution we also present the static quark potential and calculate the running coupling constant from the ghost-gluon vertex.

Figure 1

Left panel: the gluon energy $\omega (k)$ and the modulus of the scalar curvature $\chi (k)$. Right panel: the difference $\omega (k)-\chi (k)$.

Figure 2

Left panel: $d(k)$. Right panel: the functions $\omega (k)$ and $d(k)$ for different values of $\omega (\mu )$.

Figure 3

(Left) The running coupling $\alpha (k)$. (Right) The Coulomb potential $V(r)$.