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 adj. Not abelian.
Etymologies
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Examples

All this still works when we add charged matter and/or go to the nonabelian theory, but the formula for G changes.

And constructing 4d nonabelian gauge theory rigorously is thought to be a very hard problem; you can get a million dollars from the Clay Foundation if you solve it.

The problem with trying to find a rigorous mathematical construction of quantum field theory (in four dimensions) is that there is considerable evidence that such a construction does not exist: with the exception of nonabelian gauge theories, all 4d quantum field theories are believed to be “trivial”, that is, they become freefield theories in the limit that the cutoff is removed.

“The problem with trying to find a rigorous mathematical construction of quantum field theory (in four dimensions) is that there is considerable evidence that such a construction does not exist: with the exception of nonabelian gauge theories, all 4d quantum field theories are believed to be “trivial”, that is, they become freefield theories in the limit that the cutoff is removed.”

They invented a theory that, for several decades, seemed to be a total crock in terms of any relation to data  nonabelian gauge theory.

No one has rigourously constructed the quantum theory of any nonabelian gauge theory.

Rev. D 5, 1972, p. 31373155 for giving the first “understandable” demonstration that QFT for nonabelian gauge fields (and with spontaneously broken gauge symmetry) is viable.

But thanks to them we now know that QFT (for nonabelian gauge fields) * is* the correct description of nature at the subatomic level; it provides wonderful selfcontained framework with very few free parameters, and, as mentioned earlier, is just too successful.

Once again, the only meaning I know how to attach to a “nontrivial representation of the gauge group” involves violations of Gauss’ Law (in both the abelian and nonabelian cases, irrespective of whether the matter is chiral) that would definitely show up in perturbation theory.

In the nonabelian case, nontrivial representations will violate (as far as I can see) the nonabelian version of Gauss’ Law.
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