  We develop a non-perturbative framework to incorporate gauge field
fluctuations into QED3 effective actions in the infrared by fermionic
particle-vortex duality. The utility is demonstrated by the application to
models containing N species of 2-component Dirac fermions in a couple of
solvable and interpretable electromagnetic backgrounds: N = 1 or 2. For the N =
1 model, we establish a correspondence between fermion Casimir energy at finite
density and the magnetic Euler-Heisenberg Lagrangian, and we further evaluate
the correction to their amplitudes. This in turn predicts the amplification of
charge susceptibility and the reduction of magnetic permeability. We
additionally supply physical interpretations to each component of our
calculation as well as alternative derivations based on energy density
measurements in different characteristic lengths. For N = 2, we show that the
magnetic catalysis is erased in a U(1)$\times$U(1) QED3 and therefore there is
no breakdown of chiral symmetry. Some reasoning is offered based on the
properties of the lowest Landau level wave functions.
