nonabelian

“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 free-field theories in the limit that the cutoff is removed.”

String Theory is Losing the Public Debate Sean 2007

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

String Theory is Losing the Public Debate Sean 2007

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

String Theory is Losing the Public Debate Sean 2007

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 free-field theories in the limit that the cutoff is removed.

String Theory is Losing the Public Debate Sean 2007

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.

String Theory is Losing the Public Debate Sean 2007

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

The String Theory Backlash Sean 2006

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 self-contained framework with very few free parameters, and, as mentioned earlier, is just too successful.

The Greatest Physics Paper! cjohnson 2005

Rev. D 5, 1972, p. 3137-3155 for giving the first “understandable” demonstration that QFT for nonabelian gauge fields (and with spontaneously broken gauge symmetry) is viable.

The Greatest Physics Paper! cjohnson 2005

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.

String Theory is Losing the Public Debate Sean 2007

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

String Theory is Losing the Public Debate Sean 2007