Monopoles in Lattice QCD with Abelian Projection as Quantum Monopoles

TL;DR

This paper investigates quantum monopoles in lattice QCD through Abelian Projection, starting from classical solutions and applying a modified quantization technique to obtain nondivergent monopole-like configurations.

Contribution

It introduces a novel application of a modified Heisenberg quantization to classical SU(2) solutions, producing monopole-like configurations in lattice QCD.

Findings

Classical solutions with diverging energy density are quantized to produce finite monopole-like configurations.

Application of Feynman path integration yields nondivergent monopole solutions after Abelian Projection.

The method bridges classical solutions and quantum monopoles in lattice QCD.

Abstract

Within the context of the Abelian Projection of QCD monopole-like quantum excitations of gauge fields are studied. We start with certain classical solutions, of the SU(2) Yang-Mills field equations, which are not monopole-like and whose energy density diverges as $r \to \infty$. These divergent classical solutions are then quantized using a modified version of Heisenberg's quantization technique for strongly interacting, nonlinear fields. The modified Heisenberg quantization technique leads to a system of equations with mixed quantum and classical degrees of freedom. By applying a Feynman path integration over the quantum degrees of freedom the quantum-averaged solution gives a nondivergent, monopole-like configuration after Abelian Projection.