On the non-Abelian Stokes theorem in SU(2) gluodynamics

Nowadays, there are quite a few formulations of non-Abelian Stokes theorem (NAST) available (for review see, e.g., Ref. [1] and references therein). Generically there exist two principal approaches, the operator [2] and the pathintegral [3] one. We consider a new version of non-Abelian Stokes theorem [4] for SU(2) valued Wilson loops in the fundamental representation. The basic idea is to introduce the instant color orientation of the chromo-magnetic flux piercing the loop, which allows us to avoid the path ordering and represent the Wilson loop phase as an ordinary integral to which Abelian Stokes theorem applies. ConsiderWilson loopW (T ) in the fundamental representation evaluated on a closed contour C = {xμ(t), t ∈ [0;T ], xμ(0) = xμ(T )}, parameterized by xμ(t). By definition W (T ) provides a solution to the following Schrödinger like equation