Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Renormalizability of the Standard Model

  1. Aug 17, 2014 #1
    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.

    We know the Standard Model has to 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.
  2. jcsd
  3. Aug 26, 2014 #2
    I'm sorry you are not generating any responses at the moment. Is there any additional information you can share with us? Any new findings?
  4. Aug 27, 2014 #3


    User Avatar
    Gold Member

    When the only tool that you have is a hammer, every problem looks like a nail. In fact, this is a pretty good approach as long as you live in a world where all of your problems are in fact nails.

    Gauge theories have worked to explain all three of the Standard Model forces with exquisite accuracy in a way that respects special relativity. It would be odd for a non-gauge theory that is more fundamental to produce this result. Given the successes to date, it makes sense to look for a solution of the same type until someone comes up with a better alternative.

    The fact that the gauge coupling constants tend to converge around a GUT scale also suggests that all three SM forces might simply be different aspects of the same more fundamental gauge theory, just as the electric force and magnetic force turn out to be different aspects of the same thing at a more fundamental level.

    Of course, if some other part of nature, such as gravity, cannot be accurately described by a gauge theory, then attempts to do so are a case of barking up the wrong tree and we need to start looking for a screwdriver.
    Last edited: Aug 27, 2014
  5. Aug 28, 2014 #4


    User Avatar
    Science Advisor

  6. Sep 2, 2014 #5
    The original motivation came from quantum mechanics. A wave function is only determined up to global phse transformations. A shift of the phase is a symmetry of the theory and by using Noether, the corresponding Noether current is the charge density with the charge as conserved quantity.
    Now Weyl was asking to determine the phase of the wave function at least locally. Then the theory was invariant w.r.t. to a local phase transformations if one introduces a U(1) gauge field fulfilling the Maxwell equations. One automatically obtains the coupling between wave function and electromagnetic field (via a covariant derivative) and also the field equations for the elctromagnetic field.
    This idea goes over to degenerated quantum systems and one obtains non-abelian gauge theories (with groups SU(n)).
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook