Attractive Forces Between Electrons in QED$_{3}$
  Vacuum polarization effects are non-perturbatively incorporated into the photon propagator to eliminate the severe infrared problems characteristic of QED$_3$. The theory is thus rephrased in terms of a massive vector boson whose mass is $e^2/(8\pi)$. Subsequently, it is shown that electron-electron bound states are possible in QED$_3$. 
H. O. Girotti, M. Gomes, J. L. deLyra, R. S. Mendes, J. R. S.   Nascimento and A. J. da Silva