The answer to this question and the comments on it implies that general relativity has not been rigorously shown to be non-renormalizable for all loop diagrams -- only shown for two loops. However, doesn't this paper give a complete proof that GR is non-renormalizable without referring to the two-loop computation mentioned in the question's answer?
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The answer to this is potentially "yes". That's not a good SE question. – ACuriousMind Jul 11 '15 at 11:42