  We represent QCD at the hadronic scale by means of an effective Hamiltonian,
H, formulated in the Coulomb gauge. As in the Nambu-Jona-Lasinio model, chiral
symmetry is dynamically broken, however our approach is renormalizable and also
includes confinement through a linear potential with slope specified by lattice
gauge theory. We perform a comparative study of alternative many-body
techniques for approximately diagonalizing H: BCS for the vacuum ground state;
TDA and RPA for the excited hadron states. We adequately describe the
experimental meson and lattice glueball spectra and perform the first
relativistic, three quasiparticle calculation for hybrid mesons. In general
agreement with alternative theoretical approaches, we predict the lightest
hybrid states near but above 2 GeV, indicating the two recently observed
$J^{PC} = 1^{-+}$ exotics at 1.4 and 1.6 GeV are of a different, perhaps four
quark, structure. We also detail a new isospin dependent interaction from
$q\bar{q}$ color octet annihilation (analogous to ortho positronium) which
splits I = 0 and I = 1 states.
