Monopoles in Lattice QCD with Abelian Projection as Quantum Monopoles

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.