  We provide an example of nonlocal scalar electrodynamics that allows the same
Higgs mechanism so successful in local field theory. The nonlocal action is
structured in order to have the same exact solutions and the same equations of
motion for perturbations of the local theory, at any perturbative order.
Therefore, the perturbative degrees of freedom that propagate in the unstable
vacuum are reshuffled when the stable vacuum is replaced in the EoM, but their
number does not change at any perturbative order, and their properties are the
same like in the usual local theory. Finally, the theory is
super-renormalizable or finite at quantum level.
