  In this work we discuss the effect of the quartic fermion self-interaction of
Thirring type in QED in D=2 and D=3 dimensions. This is done through the
computation of the effective action up to quadratic terms in the photon field.
We analyze the corresponding nonlocal photon propagators nonperturbatively in %
\frac{k}{m}, where k is the photon momentum and m the fermion mass. The poles
of the propagators were determined numerically by using the Mathematica
software. In D=2 there is always a massless pole whereas for strong enough
Thirring coupling a massive pole may appear . For D=3 there are three regions
in parameters space. We may have one or two massive poles or even no pole at
all. The inter-quark static potential is computed analytically in D=2. We
notice that the Thirring interaction contributes with a screening term to the
confining linear potential of massive QED_{2}. In D=3 the static potential must
be calculated numerically. The screening nature of the massive QED$_{3}$
prevails at any distance, indicating that this is a universal feature of % D=3
electromagnetic interaction. Our results become exact for an infinite number of
fermion flavors.
