A Generalized Electrodynamics Part I—Non-Quantum

If one wishes to derive generalized field equations from a Lagrangian, at the same time preserving the linear character of the equations, one must admit terms involving derivatives of the field quantities. It turns out that the only non-trivial generalization of this kind, leading to differential equations of order below eighth, is obtained by taking ${L}f=({1}{8{π}}){1/2{F}_{{α}{{β}}²}+{a}²{({{∂}{F}_{{α}{β}}}{{∂}{x}_{{β}}})}²}$. This leads to a theory that contains the Land\'e-Thomas theory and accounts for the choice of sign required when one wishes to consider the total field as consisting of the Maxwell-Lorentz and the Yukawa fields.