Lattice Coulomb Hamiltonian and Static Color-Coulomb Field

Abstract

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.

110 pages + 1 fig., uuencoded compressed tar-file (190 kb) revised and shortened for readability. Technical derivations relegated to appendices. Concepts clarified in Introduction and Conclusion. One figure added

References in corpus (2)

• Landau gauge within the Gribov horizon
• Zooming-in on the SU(2) fundamental domain

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