Infinity Suppression in Gravity-Modified Electrodynamics. II

It is argued that the use of a visibly localizable parametrization of the gravitational interaction yields a number of advantages. First, the question of ambiguities can be completely solved: According to a theorem of Lehmann and Pohlmeyer there exists in such theories a unique "minimally singular" solution which it is natural to adopt as the physical one. Second, it is possible to show that this solution satisfies the usual requirements of analyticity and unitarity in the sense of perturbation theory. These points are reviewed in this paper, the main object of which is to introduce a new technique for the treatment of those nonpolynomial Lagrangians in which the interaction terms are intimately associated with the free part and contain derivatives. The gravity-modified theories exemplify this type of Lagrangian: In such theories the zero-graviton approximant to any process is "cradled" in a sequence of graphs with arbitrarily large numbers of gravitons whose sum exists, is finite, and free of ambiguities. Since the problem of preserving electromagnetic (and gravitational) gauges is also the problem of derivatives occurring either in interaction Lagrangians or in the propagators, our general treatment of derivatives is expected to resolve such gauge difficulties. In particular, we show that both the gravity-modified photon renormalization constant and the gravity-modified electromagnetic self-mass of the electron up to order $\alpha log{G}_N{m}^2$ (where $G_N$ is the Newtonian constant) are gauge-invariant.