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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?

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  • $\begingroup$ if I am not mistaken in 2D QED (Schwinger model) there are only confined fermions; how might we then even define a scattering matrix, when there are no asymptotically free states at infinity? $\endgroup$
    – Carlo Beenakker
    Commented Sep 19, 2016 at 13:11
  • $\begingroup$ @CarloBeenakker: I am not well familiar with the Schwinger model, but my impression was that in this model fermions are massless. I did not assume that in my question. I believe this assumption may lead to some extra divergences in the S-matrix. $\endgroup$
    – asv
    Commented Sep 19, 2016 at 13:20
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    $\begingroup$ for the scattering matrix in the massive Schwinger model see this article $\endgroup$
    – Carlo Beenakker
    Commented Sep 19, 2016 at 13:29
  • $\begingroup$ @CarloBeenakker: Thanks for the relevant reference. It is not self contained, so it may take me some time to figure out whether it contains answers to my questions. $\endgroup$
    – asv
    Commented Sep 19, 2016 at 14:59
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    $\begingroup$ You might want to take a look at the book Non-Perturbative Methods in 2 Dimensional Quantum Field Theory by Abdalla, Abdalla and Rothe. That should be selfcontained and certainly discusses exact S-matrices and 2d QED, so the answer to your questions might be in there. $\endgroup$
    – Jules Lamers
    Commented Sep 20, 2016 at 9:39

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