  We discuss the derivation of the path integral representation over gauge
degrees of freedom for Wilson loops in SU(N) gauge theory and 4-dimensional
Euclidean space-time by using well-known properties of group characters. A
discretized form of the path integral is naturally provided by the properties
of group characters and does not need any artificial regularization. We show
that the path integral over gauge degrees of freedom for Wilson loops derived
by Diakonov and Petrov (Phys. Lett. B224 (1989) 131) by using a special
regularization is erroneous and predicts zero for the Wilson loop. This
property is obtained by direct evaluation of path integrals for Wilson loops
defined for pure SU(2) gauge fields and Z(2) center vortices with spatial
azimuthal symmetry. Further we show that both derivations given by Diakonov and
Petrov for their regularized path integral, if done correctly, predict also
zero for Wilson loops. Therefore, the application of their path integral
representation of Wilson loops cannot give "a new way to check confinement in
lattice" as has been declared by Diakonov and Petrov (Phys. Lett. B242 (1990)
425). From the path integral representation which we consider we conclude that
no new non-Abelian Stokes theorem can exist for Wilson loops except the
old-fashioned one derived by means of the path-ordering procedure.
