Quantum field-theoretical electromagnetic and gravitational two-particle potentials

The fourth-order static electromagnetic and gravitational two-particle potentials are derived from the scattering operator by using the techniques of the standard field theory. Integrals over four-vector variables are evaluated in a covariant manner, while in earlier treatments such integrals are usually converted to noncovariant forms. Our treatment is more direct, and we are able to carry out regularization and renormalization of divergent integrals unambiguously where necessary. Moreover, calculations of multiple parameter integrals are reduced to elementary integrations in the static and long-range approximations. Our quantum field-theoretical results are in complete agreement with the classical potentials