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I was reading a book by Franco Strocchi, this one, and in some points the author claims that the case of $d=3+1$ of triviality of $\phi^4$ theory is now proven. As far as I can tell, we have just some evidence from lattice computations. Am I missing any relevant reference about this matter?

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  • $\begingroup$ Can you explain what you mean by triviality? $\endgroup$ – Prahar Oct 23 '17 at 15:09
  • $\begingroup$ Can you also add on what page this statement is made? $\endgroup$ – DanielC Oct 23 '17 at 15:15
  • $\begingroup$ @DanielC You can find the statement on page 38 starting with "The recent proof of triviality...". $\endgroup$ – Jon Oct 23 '17 at 18:01
  • $\begingroup$ @Prahar A simple presentation of triviality is given at en.wikipedia.org/wiki/Quantum_triviality. My preferred one uses the form of the propagator that is Yukawa-like or a sum of Yukawas and all the part of the spectrum with bound states just missing considering a Källén-Lehmann representation. $\endgroup$ – Jon Oct 23 '17 at 18:04
  • $\begingroup$ @prahar Triviality in this context means that the continuum limit of the lattice theory only exists for the free theory. $\endgroup$ – user1504 Oct 27 '17 at 17:29

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