Page "Regularization (physics)" Paragraph 22

The path-integral formulation provides the most direct way from the Lagrangian density to the corresponding Feynman series in its Lorentz-invariant form.

The free-field part of the Lagrangian density determines the Feynman propagators, whereas the rest determines the vertices.

As the QED vertices are considered to adequately describe interactions in QED scattering, it make sense to modify only the free-field part of the Lagrangian density so as to obtain such regularized Feynman series that the Lehmann-Symanzik-Zimmermann reduction formula provides a perturbative S-matrix that: ( i ) is Lorentz invariant and unitary ; ( ii ) involves only the QED particles ; ( iii ) depends solely on QED parameters and those introduced by the modification of the Feynman propagators — for particular values of these parameters it is equal to the QED perturbative S-matrix ; and ( iv ) exhibits the same symmetries as the QED perturbative S-matrix.

Let us refer to such a regularization as the minimal realistic regularization, and start searching for the corresponding, modified free-field parts of the QED Lagrangian density.