Infrared divergence enforces a rearranged perturbation expansion I Scalar electrodynamics

It is shown that the ordinary perturbation expansion must, except in certain cases, be rearranged in order to carry out uniquely the infrared exponentiation in a translation- and gauge-invariant way. The uniqueness of the exponent of order alpha follows from requiring exact order-by-order agreement with the OPE before summation and also from requiring that the exponentiation of all factorizable parts must be done before integration. By this rearrangement the remaining infrared- regular part is defined in terms of correlations with respect to photon momenta in the integrands. Radiative corrections are included and the renormalization of this correlation rearrangement is carried through. All photons are treated identically. (23 refs).