Wave function renormalization

Wave function renormalization is the rescaling of quantum fields so that the Lehmann weight of its quanta is 1. (It's trickier to define it for unstable particles). This is one possible wave function renormalization which happens to be scale independent.

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 ${\sqrt {Z}}$. A scale dependent wavefunction renormalization for a field means that that field has an anomalous scaling dimension.