For example, at low energies the interaction of a photon with a nucleon is a very complicated calculation involving interactions between the photon and a sea of quarks and gluons, and often the calculation cannot be fully performed from first principles.
However, the generic Lorentz-invariant form of the matrix element for the electromagnetic current interaction is known, where
This matrix element then serves to determine the transition amplitude involved in the scattering interaction or the respective particle decay—cf.
In general, the Fourier transforms of form factor components correspond to electric charge or magnetic profile space distributions (such as the charge radius) of the hadron involved.
The analogous QCD structure functions are a probe of the quark and gluon distributions of nucleons.