In quantum gravity, I get 'mixed signals' as regards renormalizability. My state of confusion is being caused, I suspect, by an incomplete understanding of what is covered under t'Hooft's 1972 proof that non-Abelian gauge theories are renormalizable. ( = Nobel Prize 1999).(adsbygoogle = window.adsbygoogle || []).push({});

Specifically, some say that GR can be formulated as a non-Abelian gauge theory (see Moshe Carmeli, 'Group Theory and General Relativity', or his book 'Classical Fields: General Relativity and Gauge Theory'). Carmeli, in his classical GR developments makes a comment to the effect that t'Hooft's work implies that GR should be renormalizable. (his work is from the 1970s).

Yet, I am not aware of any work (over the past 40 years) that extends this 'GR as a non-Abelian gauge theory' into the quantum realm, as a renormalizable gauge theory. This leads me to think that there are finer points to the whole framework of renormalization of non-Abelian gauge theories that I don't fully understand: certain caveats, perhaps, in t'Hooft's proof that disqualify GR from renormalization. For example, Carmeli expresses things in terms of the group GL(2,C) in place of SU(2) (standard Yang Mills). GR imposes other issues (nature of the observer, four dimensions etc).

Fast forward to 2017 and quantum GR is considered a good candidate for an effective field theory, which reinforces the notion that renormalization is an impossibility, non-Abelian gauge theory or no.

Does anyone have insight into how we make ends meet here?

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# A Quantum Gravity: Renormalization vs. Effective Field Theory

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