I am not completely sure that this question is appropriate for this site, but I have asked a similar question here https://physics.stackexchange.com/questions/271372/s-matrix-in-qed-in-2d-space-time and did not get an answer. Also on this site I got in the past some nice answers to questions related to physics.

I am interested in the S-matrix in QED in 2-dimensional Minkowski space-time.

1) Do I understand correctly that In and Out states of physical interest in the 2d case include fermions only (because photons have no physical polarizations)?

2) Is it possible to compute the S-matrix  perturbatively like in the classical 4d case? If yes, what is the propagator of the free EM field?