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Let us assume that one would like to compute perturbatively amplitudes of various processes in QED in 2-dimensional space-time in analogy to the well known 4d case.

Is it possible? What should be the free photon propagator in that case?

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  • $\begingroup$ Related: physics.stackexchange.com/q/32685/2451 and links therein. $\endgroup$ – Qmechanic Aug 10 '16 at 15:55
  • $\begingroup$ @Qmechanic: Thank you, but apparently they do not discuss the photon propagator. $\endgroup$ – MKO Aug 10 '16 at 16:35
  • $\begingroup$ As said in the linked answer, 1D+1D doesn't work, but there are these 1.5D and 2.5D approaches releated to plasma physics which solve Maxwell like equations with 'magnetic field pointing out of dimensions' or something like that. $\endgroup$ – Mikael Kuisma Aug 10 '16 at 19:20
  • $\begingroup$ @MikaelKuisma: I am not sure that the 1+1 case does not work at all since there is the Schwinger model which is QED in this case. But I did not see that pertubative methods are used in its context. $\endgroup$ – MKO Aug 11 '16 at 3:37
  • $\begingroup$ @MKO The answer of Ron Maimon covers Schwinger model and other answer handles 1+1 case as well to show that only constant electric fields are allowed. But yeah, that only forbids propagation of light, but not solving the propagator, so you're right. $\endgroup$ – Mikael Kuisma Aug 11 '16 at 8:01

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