Scale Invariance in Quantum Field Theory
The scale-dependence of a quantum field theory (QFT) is characterised by the way its coupling parameters depend on the energy-scale of a given physical process. This energy dependence is described by the renormalization group, and is encoded in the beta-functions of the theory.
For a QFT to be scale-invariant, its coupling parameters must be independent of the energy-scale, and this is indicated by the vanishing of the beta-functions of the theory. Such theories are also known as fixed points of the corresponding renormalization group flow.
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