Why is it such a big deal? According to the "modern" (Wilsonian) viewpoint, non-renormalizability is not such a "sickness" of a quantum field theory, as long as one adopts the viewpoint that the theory is not UV complete, aka, the theory is simply an effective field theory with a finite cut-off.(adsbygoogle = window.adsbygoogle || []).push({});

We know the Standard Modelhasto be incomplete. I've heard a lot (e.g. S. Coleman's Aspects of Symmetry) that physicists like gauge theories because they belong to rare class of interacting field theories that happen to be renormalizable in four dimensions.

The reason I'm asking today is because I was reading this paper by 't Hooft-- it's a historical account for his famous proof that gauge theories are renormalizable. He talks about how the challenges to unitarity due in a theory of massive vector bosons, and then talks about how it is solved by the Higgs potential. The same content is the subject of Chapt. 21 of Peskin and Schroeder. I think the idea is there is a subtle interplay between gauge degrees of freedom and spontaneous symmetry breaking. It seems miraculous that it is actually possible to show that gauge theories are consistent despite the various ways that unphysical degrees of freedom could threaten consistency. I guess the question I am really asking then is, why should a fundamental theory take the form of a gauge theory?

I feel like I should know this one, but I'm struggling to connect the dots at the moment.

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# Renormalizability of the Standard Model

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