WKB-like wave-functional for a string state and path-dependent phase factor

The variational calculation of the path-ordered phase factor is streamlined. We propose that the wave functional for a string state is approximately of the form

$\text{Ψ[x(σ)=}\text{Π}\text{σ′}\text{K(x(σ′))}\text{P exp}\text{ie∫}\text{A d}\text{x}$

.The real factor K is shown to be proportional to the square root of the dielectric permeability in the Kogut-Susskind-'t Hooft model of colour flux collimation.