Covariant time-ordered perturbation theory

By reformulating Kadyshevskys perturbation theory for the S matrix in quantum field theory, a covariant version of time-ordered perturbation theory is obtained. The new graphical rules are just like those of time-ordered perturbation theory except for the replacement of three-momentum-conserving functions with covariant three-dimensional functions and the use of invariant denominators instead of energy denominators. The new rules are illustrated by deriving an approximate three-dimensional integral equation which describes the scattering of two identical scalar particles which interact by exchanging a different scalar particle.