Engineering dimensions of relativistic fields ($[\varphi ]=(d-2)/2,[\psi ]=(d-1)/2,[A_{\mu }]=(d-2)/2$)

Canonical free scalar and gauge-vector kinetic terms contain two derivatives and two fields, whereas the Dirac kinetic term contains one derivative and two spinor fields. Matching their mass dimension to $d$ in $d$ spacetime dimensions gives the displayed engineering dimensions. These are the dimensions used in power counting; interacting scaling dimensions can additionally contain anomalous contributions.