ar X iv : h ep - t h / 04 10 07 1 v 2 3 1 D ec 2 00 4 DIVERGENCE OF THE 1 N f - SERIES EXPASION IN QED

The perturbative expansion series in coupling constant in QED is divergent and is expected to be, at the best, conditionally convergent. The 1/Nf series expansion, where Nf is the number of flavours, defines a rearrangement of this perturbative series, and therefore, its convergence would serve as a proof that the perturbative series is, in fact, conditionally convergent.Unfortunately, the 1/Nf series also diverges.We proof this using arguments similar to those of Dyson. We expect that some of the ideas and techniques discussed in our paper will find some use in proving that the perturbation series in coupling constant is conditionally convergent. PACS numbers:03.65.-w,11.01.-z,12.20.-m