Scale invariance
= Scale invariance
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A law or statistical object is scale invariant if its form is unchanged by rescaling lengths, with any specified scaling weight for the fields. A dimensionless field's three-dimensional nonzero-mode <power spectrum> obeys $P(\lambda k)=\lambda^{-3}P(k)$ when its statistics have this scaling. The meaning of invariance must specify whether zero modes and regulators are being transformed.