Abstract
We will calculate the cross-section for annihilation in two photons of an electron-positon pair with a simple modification of the electronic propagator. In order to conserve the gauge invariance, besides the modification of the vertex prescribed by the Ward-Takahashi identity and proposed by McClure and Drell, also the intervention of a two-photon vertex is considered. First the problem of the general construction of such vertex is dealt with; afterwards, we apply this result, in the simplest form, to compute differential and total cross-sections. The calculation is done in view of the experiments of pair annihilation planned in order to test in this way the validity of quantum electrodynamics.
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