  We consider reduced quantum electrodynamics (RQED$_{d_\gamma,d_e}$) a model
describing fermions in a $d_e$-dimensional space-time and interacting via the
exchange of massless bosons in $d_\gamma$-dimensions ($d_e \leq d_\gamma$). We
compute the two-loop mass anomalous dimension, $\gamma_m$, in general
RQED$_{4,d_e}$ with applications to RQED$_{4,3}$ and QED$_4$. We then proceed
on studying dynamical (parity-even) fermion mass generation in RQED$_{4,d_e}$
by constructing a fully gauge-invariant gap equation for RQED$_{4,d_e}$ with
$\gamma_m$ as the only input. This equation allows for a straightforward
analytic computation of the gauge-invariant critical coupling constant,
$\alpha_c$, which is such that a dynamical mass is generated for $\alpha_r >
\alpha_c$, where $\alpha_r$ is the renormalized coupling constant, as well as
the gauge-invariant critical number of fermion flavours, $N_c$, which is such
that $\alpha_c \rightarrow \infty$ and a dynamical mass is generated for $N <
N_c$. For RQED$_{4,3}$, our results are in perfect agreement with the more
elaborate analysis based on the resolution of truncated Schwinger-Dyson
equations at two-loop order. In the case of QED$_4$, our analytical results
(that use state of the art five-loop expression for $\gamma_m$) are in good
quantitative agreement with those obtained from numerical approaches.
