  We discuss how to implement, in lattice gauge theories, external charges
which are not commensurate with an elementary gauge coupling. It is shown that
an arbitrary, real power of a standard Wilson loop (or Polyakov line) can be
defined and consistently computed in lattice formulation of non-abelian, two
dimensional gauge theories. However, such an observable can excite quantum
states with integer fluxes only. Since the non-integer fluxes are not in the
spectrum of the theory they cannot be created, no matter which observable is
chosen. Also the continuum limit of above averages does not exist unless the
powers in question are in fact integer. On the other hand, a new continuum
limit exists, which is rather intuitive, and where above observables make
perfect sense and lead to the string tension proportional to the square of
arbitrary (non necessary commensurate with gauge coupling) charge.
