Schwinger-DeWitt proper-time expansion and eikonal approximation.

Abstract

In the context of the Dirac equation, we show that the Schwinger-DeWitt proper-time expansion of the exact Green's function is useful for high-energy scattering and, in fact, provides a systematic generalization of the eikonal approximation. Because of its simplicity and its direct appeal to the coordinate-space scattering picture, the Schwinger-DeWitt expansion method should be valuable in studying corrections to the lowest-order eikonal approximation. A numerical comparison is made for an exponential potential. Within the same framework a systematic formalism is also developed to deal with large-angle scattering, and this yields a generalization of Schiff's large-angle formula. Applications to high-energy scattering problems in quantum field theories are indicated.