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 L₅= (18) 1{2F^{2}+a^2 ({{F_}{x_}) }^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.