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Is the Einstein–Cartan theory renormalizable?

  1. May 11, 2015 #1
    Specially regarding the Sciama-Kibble take on the matter; I've come by this paper http://dx.doi.org/10.1063/1.1703702 recently, and, though I haven't read it in its entirety, the reasonings it presents make a lot of physical sense to me.
    I'm not terribly curious as to what happens if you use a more general affine connection than in GR (though, one will deal with this if one has to; remember that Einstein, for instance, assumed null torsion while deriving the EFE basically for mathematical simplicity - cf. The Collected Papers of Albert Einstein, VOL 6, DOC. 30, The Foundation of the General Theory of Relativity); what holds sway on me is the close analogy with the YM gauge principle - and, of course, whether or not it can be quantized.
    I understand that the EC-SK equations reduce to the EFE for null torsion (if not, they most certainly should!), so there wouldn't be no a priori reason to hope the gravitational field is renormalizable here. So here we are: does the introduction of torsion magically make the theory renormalizable (and 'therefore' quantizable)? If not, what specifically prevents it from being so? (this last question is more general in scope - what makes a theory renormalizable? -, if you'll care to develop; however, I should probably mention I'm still very green in this renormalization biz, and such a discussion can get potentially off-topic).
     
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  3. May 11, 2015 #2

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