Color-Coulomb Force Calculated from Lattice Coulomb Hamiltonian
Attilio Cucchieri, Daniel Zwanziger (New York University)
TL;DR
This paper computes the static color-Coulomb potential from a lattice gauge theory Hamiltonian, showing qualitative agreement with theoretical expectations and semi-quantitative agreement with lattice and phenomenological results.
Contribution
It derives and solves a non-linear integral equation for the color-Coulomb potential within the Coulomb Hamiltonian framework on the lattice, incorporating Gribov horizon restrictions.
Findings
Potential is Coulombic with logarithmic short-range corrections.
Long-range potential exhibits confinement behavior.
Results semi-quantitatively agree with lattice and phenomenological data.
Abstract
The static color-Coulomb potential is calculated as the solution of a non-linear integral equation. This equation has been derived recently as a self-consistency condition which arises in the Coulomb Hamiltonian formulation of lattice gauge theory when the restriction to the interior of the Gribov horizon is implemented. The potential obtained is in qualitative agreement with expectations, being Coulombic with logarithmic corrections at short range and confining at long range. The values obtained for the string tension and are in semi-quantitative agreement with lattice Monte Carlo and phenomenological determinations.
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