On the decomposition of the Feynman propagator

The Feynman propagator, in momentum representation, is a four-dimensional transform over space and time variables. If the space and time integrations are performed separately, the propagator can be decomposed into two parts, one corresponding to positive and the other to negative energy intermediate state. By the use of this decomposed propagator, the relative contributions of the positive and negative energy intermediate states to the matrix element can be estimated. For example in Compton scattering it leads to the apparently paradoxical result that in the “nonrelativistic approximation” it is only the negative energy intermediate state that contributes to the matrix element.