Editing Quantum electrodynamics (section)

==Nonconvergence of series==
An argument by [[Freeman Dyson]] shows that the [[radius of convergence]] of the perturbation series in QED is zero.<ref>{{Cite web
  | last = Kinoshita
  | first = Toichiro
  | title = Quantum Electrodynamics has Zero Radius of Convergence Summarized from Toichiro Kinoshita
  | date = June 5, 1997
  | url = http://www.lassp.cornell.edu/sethna/Cracks/QED.html
  | access-date = May 6, 2017
}}</ref> The basic argument goes as follows: if the [[fine-structure constant|coupling constant]] were negative, this would be equivalent to the [[Coulomb force constant]] being negative. This would "reverse" the electromagnetic interaction so that ''like'' charges would ''attract'' and ''unlike'' charges would ''repel''. This would render the vacuum unstable against decay into a cluster of electrons on one side of the universe and a cluster of positrons on the other side of the universe. Because the theory is "sick" for any negative value of the coupling constant, the series does not converge but is at best an [[asymptotic series]].

From a modern perspective, we say that QED is not well defined as a quantum field theory to arbitrarily high energy.<ref>{{cite journal
  | last = Espriu and Tarrach
  | title = Ambiguities in QED: Renormalons versus Triviality
  | date = Apr 30, 1996
  | arxiv = hep-ph/9604431
  | doi=10.1016/0370-2693(96)00779-4
  | volume=383
  | issue = 4
 | journal=Physics Letters B
  | pages=482–486
| bibcode=1996PhLB..383..482E| s2cid = 119095192
 }}</ref> The coupling constant runs to infinity at finite energy, signalling a [[Landau pole]]. The problem is essentially that QED appears to suffer from [[quantum triviality]] issues. This is one of the motivations for embedding QED within a [[Grand Unified Theory]].