Erratum: Acta Physica Polonica. B, 2015, Vol. 46, Iss. 4, p.905

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 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.