On classical scalar field theories and the relativistic kepler problem

Abstract

Two versions of classical relativistic field theory corresponding to massless scalar exchange are compared. It is found that they lead to identical field equations but different equations of motion. The motion of one particle bound by the field of another, infinitely massive particle, i.e., the Kepler problem, is examined. In one case the path is an ellipse precessing through an angle equal to minus one-sixth the value predicted by general relativity. In the other case the path is an ellipse which does not precess. The relativistic Kepler problem in the latter case is identical to that formulated by Fronsdal, who started from an approximation to the Bethe-Salpeter equation.