  We give a gauge-independent definition of magnetic monopoles in the $SU(N)$
Yang-Mills theory through the Wilson loop operator. For this purpose, we give
an explicit proof of the Diakonov-Petrov version of the non-Abelian Stokes
theorem for the Wilson loop operator in an arbitrary representation of the
$SU(N)$ gauge group to derive a new form for the non-Abelian Stokes theorem.
The new form is used to extract the magnetic-monopole contribution to the
Wilson loop operator in a gauge-invariant way, which enables us to discuss
confinement of quarks in any representation from the viewpoint of the dual
superconductor vacuum.

High Energy Physics - Theory;High Energy Physics - Phenomenology