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Asymptotic safety and local gauge invariance

  1. Sep 5, 2014 #1
    Hi folks -- does anyone know of a good survey article on the topic of whether local gauge invariance is a requirement of a fundamental theory within QFT -- hence of an asymptotically safe theory?

    I only have a few scattered remarks to this effect (by F. Wilczek mostly), so any good references or even statements of the state of play would be most appreciated!
  2. jcsd
  3. Sep 5, 2014 #2


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    Gauge invariance is not a fundamental requirement for a nonlinear relativistic quantum field theory that rigourously exists, at least not in all dimensions. For example, http://www.claymath.org/sites/default/files/yangmills.pdf (section 6.2) says there are rigourous nonlinear scalar fields in 2 and 3 dimensions. However they go on to discuss that in 4 dimensions the best candidate for a rigourous construction seems to be Yang-Mills, which is a gauge theory.
  4. Sep 10, 2014 #3
    thank you very much, that is tremendously helpful!
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