2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/194901The 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.9 pages, 3 figures, references added.High Energy Physics - TheoryHigh Energy Physics - LatticeHigh Energy Physics - Phenomenologytext