  In any Abelian gauge theory with an action periodic in the link variables one
can perform a duality transformation not only in the partition function, but
also in correlation functions including Polyakov loops. The calculation of
expectation values in the confinement phase, like electric field strength or
monopole currents in the presence of external charges, becomes significantly
more efficient simulating the dual theory. We demonstrate this using the
ordinary Wilson action. This approach also allows a quantitative analysis of
the dual superconductor model, because the dual transformed U(1) theory can be
regarded as limit of a dual non-compact Abelian Higgs model. In this way we
also try to interpret the behaviour of monopole condensate and string
fluctuations. Finally we present some applications for simulating the dual U(1)
gauge theory.
