Engineering dimension ($[X{]}_{\mathrm{eng}}$)

The engineering dimension of a field, parameter or operator is its dimension under the rescaling that leaves the quadratic theory invariant. Interactions can change it into a full scaling dimension.

An anomalous dimension is the interaction-generated difference between a full scaling dimension and its engineering dimension. For a scalar field, momentum-dependent self-energy corrections require wave-function renormalization and produce ${\Delta }_{\varphi }=(d-2+\eta )/2$.