About scale invariance in "beyond the standard model".
At the base of the analysis is the principle of scale invariance. So what is being said: 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?
It then mentioned: "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.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 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 what is being pointed out is to something else "more interesting" as said so what is that? And finally what does he mean by "fields can scale with fractional dimensions?"