One possible wave function renormalization, which happens to be scale independent, is to rescale the fields so that the Lehmann weight (Z in the formula above) of their quanta is 1. For the purposes of studying renormalization group flows, if the coefficient of the kinetic term in the action at the scale Λ is Z, then the field is rescaled by Z . A scale dependent wave function renormalization for a field means that that field has an anomalous scaling dimension.