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QFT and scale invariance

  1. May 4, 2015 #1
    Hey guys!

    I was reading the following paper http://arxiv.org/abs/hep-ph/0703260 for Georgi and I have a conceptual question about it.

    Howard Georgi was talking about this Unparticle Physics theory and at the base of his analysis is the principle of scale invariance. So Georgi is saying what if there were another sector of the theory that interacts so weakly with the standard model that it hasn’t been noticed yet, and what if it were exactly scale-invariant?

    He then mentions: "A free massless particle is a simple example of scale invariant stuff because the zero mass is unaffected by rescaling. But quantum field theorists have long realized that there are more interesting possibilities — theories in which there are fields that get multiplied by fractional powers of the rescaling parameter."

    He adds: "It is clear what scale invariance is in the quantum field theory. Fields can scale with fractional dimensions."

    My question now is: What does he mean by that last sentence in bold? What is [scale invariance](http://en.wikipedia.org/wiki/Scale_invariance) in quantum field theory? Now I can say in QFT when electromagnetic field is quantized, there the photon has zero mass and is thus scale invariant. But he is pointing to something else "more interesting" as he said so what is that? And finally what does he mean by "fields can scale with fractional dimensions?"
     
  2. jcsd
  3. May 4, 2015 #2
    I think he just means that one can perform dimensional regularisation for renormalisation, no?
     
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