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 when its statistics have this scaling. The meaning of invariance must specify whether zero modes and regulators are being transformed.
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Scale invariance is a property of certain systems or equations where the system's characteristics or behavior do not change under a rescaling of lengths, times, or other dimensions. In other words, if you magnify or reduce the size of the system (or the parameters involved), the system remains statistically or qualitatively the same. This concept is prevalent in various fields, including physics, economics, and biology.