Covariant time-ordered perturbation theory

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Abstract
By reformulating Kadyshevsky’s 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 δ functions with covariant three-dimensional δ 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.