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When I read paper PRB89, 235431 about the effective field theory of graphene, there is a statement that QED perturbative series is only asymptotic and eventually diverges at very high orders (e. g. the second paragraph in sec. II), which I cannot understand exactly.

It is known that QED is renormalizable. Thus, why the perturbative series diverge at the orders higher than 137. Please give me some refs, thank you.

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  • $\begingroup$ We have a question about the physical meaning of the perturbation series being asymptotic and not convergent here already. I'm not sure what exactly your question is, and if it is different from that one. $\endgroup$
    – ACuriousMind
    Oct 27, 2015 at 15:36
  • $\begingroup$ @ACuriousMind I have read your question and answers. The key point you concern about is radius of convergence. In the sense of the radius of convergence, I know the coupling constant must be small such as fine structure constant. Moreover, it can be found in answer that "this argument is strictly heuristical". Thus, I guess the author of current paper PRB89, 235431 want tell us that the perturbative series would diverge ultimately, no matter what is coupling constant. $\endgroup$
    – K. Chang
    Oct 28, 2015 at 0:59

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