  Quantum electrodynamics (QED) of electrons confined in a plane and that yet
can undergo interactions mediated by an unconstrained photon has been described
by the so-called {\it pseudo-QED} (PQED), the (2+1)-dimensional version of the
equivalent dimensionally reduced original QED. In this work, we show that PQED
with a nonlocal Chern-Simons term is dual to the Chern-Simons Higgs model at
the quantum level. We apply the path-integral formalism in the dualization of
the Chern-Simons Higgs model to first describe the interaction between quantum
vortex particle excitations in the dual model. This interaction is explicitly
shown to be in the form of a Bessel-like type of potential in the static limit.
This result {\it per se} opens exciting possibilities for investigating
topological states of matter generated by interactions, since the main
difference between our new model and the PQED is the presence of a nonlocal
Chern-Simons action. Indeed, the dual transformation yields an unexpected
square root of the d'Alembertian operator, namely, $(\sqrt{-\Box})^{-1}$
multiplied by the well-known Chern-Simons action. Despite the nonlocality, the
resulting model is still gauge invariant and preserves the unitarity, as we
explicitly prove. {}Finally, when coupling the resulting model to Dirac
fermions, we then show that pairs of bounded electrons are expected to appear,
with a typical distance between the particles being inversely proportional to
the topologically generated mass for the gauge field in the dual model.
