Abelian representation for nonabelian Wilson loops and the Non - Abelian Stokes theorem on the lattice

Abstract

We derive the Abelian - like expression for the lattice SU(N) Wilson loop in arbitrary irreducible representation. The continuum Abelian representation of the SU(N) Wilson loop (for the loop without selfintersections) that has been obtained by Diakonov and Petrov appears to be a continuum limit of this expression. We also obtain the lattice variant of a non - Abelian Stokes theorem and present the explicit expression for the matrix $\cal H$ used in the Diakonov - Petrov approach.