  The recent discovery of two-dimensional Dirac materials, such as graphene and
transition-metaldichalcogenides, has raised questions about the treatment of
hybrid systems, in which electrons moving in a two-dimensional plane interact
via virtual photons from the three-dimensional space. In this case, a projected
non-local theory, known as Pseudo-QED, or reduced QED, has shown to provide a
correct framework for describing the interactions displayed by these systems.
In a related situation, in planar materials exhibiting a superconducting phase,
the electromagnetic field has a typical exponential decay that is interpreted
as the photons having an effective mass, as a consequence of the Anderson-Higgs
mechanism. Here, we use an analogous projection to that used to obtain the
pseudo-QED to derive a Pseudo-Proca equivalent model. In terms of this model,
we unveil the main effects of attributing a mass to the photons and to the
quasi-relativistic electrons. The one-loop radiative corrections to the
electron mass, to the photon and to the electron-photon vertex are computed. We
calculate the quantum corrections to the electron g-factor and show that it
smoothly goes to zero in the limit when the photon mass is much larger than the
electron mass. In addition, we correct the results obtained for graphene within
Pseudo-QED in the limit when the photon mass vanishes.
