Editing Scale invariance (section)

===Massless scalar field theory===
Free, massless [[scalar field (quantum field theory)|quantized scalar field theory]] has no coupling parameters. Therefore, like the classical version, it is scale-invariant. In the language of the renormalization group, this theory is known as the [[Gaussian fixed point]].

However, even though the classical massless ''φ''<sup>4</sup> theory is scale-invariant in ''D''&nbsp;=&nbsp;4, the quantized version is '''not''' scale-invariant. We can see this from the [[Beta function (physics)|beta-function]] for the coupling parameter, ''g''.

Even though the quantized massless ''φ''<sup>4</sup> is not scale-invariant, there do exist scale-invariant quantized scalar field theories other than the Gaussian fixed point. One example is the '''Wilson–Fisher fixed point''', below.