On the new field theory
M. H. L. Pryce · Proceedings of the Royal Society of London A Mathematical and Physical Sciences · 1936
Abstract The purpose of this paper is to derive the dynamical conditions governing the motion of point charges in the New Field Theory from the variation equation δ ∫ H√- gdx1dx2dx3dx4 = 0, of Born and infeld, where the coordinates of the charges, as well as the field strengths, are varied; also to develop the theory along lines parallel to classical mechanics, with a view to generalization to the quantum theory in a later paper. It was clear from the start of the New Field Theory (although not fully appreciated in I and II) that the motion of the charges was not governed by the field equations alone, and that some further condition had to be added. It was also clear from physical considerations of conservation of energy and momentum what this condition had to be; namely, that the total force (see § 5) on each charge must vanish. But hitherto this has not been derived from the more basic variation equation.