Quadratic Action Principle of Relativity

By an improved mathematical technique, the field equations derivable from a Lagrangian which is quadratic in the curvature components can now be studied in greater detail. The intercalation of a high-frequency metrical plateau between the flat Minkowskian metric and the macroscopic physical world has the consequence that the resulting perturbation equations are no longer of fourth but only of second order, thus making a comparison with Einstein's equations possible. The principal difference is that the free vector of Einstein's theory is now restricted by a divergence condition, with the result that the equations of the electromagnetic field, expressed in terms of the vector potential, become solutions of the macroscopic field equations. The cases of fourfold symmetry with imaginary time and 3 + 1 symmetry with real time are discussed. The gravitational phenomena and the second-order interaction terms, needed for the construction of material particles, remain outside the limits of the present investigation.