The Coulomb Gauge Hamiltonian (CGH) model, a field theoretical, relativistic, many-body approach to Quantum Chromodynamics (QCD),is developed, which describes the vacuum through a Bogoliubov-Valatin transformation. This transformation also dresses the bare quarks and gluons, producing quasi-particles with constituent masses and quark and gluon condensates. This framework is then applied, using the variational principle, to the hybrid meson and tetra-quark problems, where exotic quantum numbers can be generated; light u-ubar-g, strange s-sbar-g and charmed c-cbar-g hybrid meson spectra are calculated and found to agree reasonably well with lattice and Flux Tube predictions. The light tetra-quark spectra is also calculated, along with the charmed tetra-quark structures likely to be the X(3872) and Y(4262) particles. The lowest 1-+ hybrid meson mass is found to be just above 2.2 GeV while the lightest tetra-quark state mass with these exotic quantum numbers is predicted around 1.4 GeV. These theoretical formulations all indicate the observed 1-+ pi 1(1600) and, more clearly, pi 1(1400) are definitely not hybrid states but could be tetra-quark states, with a molecular type, meson-meson structure.