### Happy ~~Halloween~~ تحرير ليبيا

Reviving a Halloween tradition on this blog…

Reviving a Halloween tradition on this blog…

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Jacques,

I know this is off topic, but I was wondering if you wrote a post (or if you know of someone who has written such a post, or a paper) about connections between GR and gauge theory, especially arguing why GR cannot be written as a gauge theory similar to the other interactions.

Thanks.

Posted by:
unif on November 18, 2011 4:29 PM | Permalink
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Depends what you mean.

Written in terms of a metric, GR *is* a theory with a local gauge symmetry (diffeomorphisms). Presumably, thought, what you want is something formulated as a theory of connections on a $G$-principal bundle, for some suitable choice of $G$.

That sorta works in 3 dimensions, as shown long ago, by Witten. The choice of $G$ depends both on the signature and the sign of the cosmological constant. For $\Lambda=0$ and Minkowski signature, $G$ is the Poincaré group, $G=ISO(2,1)$. The action is of Chern-Simons type.

Unfortunately:

- That formulation is not easily coupled to dynamical matter.
- The natural domain of integration for the gauge theory (as subsequent evidence has shown) is peculiar, and probably not what one wants, for a theory of gravity.

Those two comments are related.

In 4 dimensions, the best you can do is based on $G=SO(4,1)$. And similar criticisms hold (modulo the fact that one doesn’t have nearly the same control over the quantum theory, as in the 3D case).

All in all, this has not proven a terribly promising avenue. I think you should ask yourself what you hope the gauge theory point of view will buy you.

Well, let’s go back to the topic, this Kadhafi pumpkin looks really great. how many time does it takes to craft it?

Thanks

Posted by:
John Abbes on December 1, 2011 4:34 PM | Permalink
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## Re: Happy Halloween تحرير ليبيا

Sorry a little late but have a nice halloween everyone!

Best regards from Ireland.