Lattice Coulomb hamiltonian and static color-Coulomb field

The lattice Coulomb-gauge hamiltonian is derived from the transfer matrix of Wilson's Euclidean lattice gauge theory, wherein the lattice form of Gauss's law is satisfied identically. The restriction to a fundamental modular region (no Gribov copies) is implemented in an effective hamiltonian by the addition of a ''horizon function'' G to the lattice Coulomb-gauge hamiltonian. Its coefficient gamma(0) is a thermodynamic parameter that ultimately sets the scale for hadronic mass, and which is related to the bare coupling constant g(0) by a ''horizon condition''. This condition determines the low momentum behavior of the (ghost) propagator that transmits the instantaneous longitudinal color-electric field, and thereby provides for a confinement-like feature in leading order in a new weak-coupling expansion.