Analytic strong-coupling expansion in 1/e for the electron propagator without fermion loops in quantum electrodynamics

Summary

Starting from the path integral for the electron propagator without fermion loops in a background electromagnetic field, we analytically derive a strong-coupling expansion in powers of 1/e. We find that in the strong-coupling limit the electron propagator is genuinely cut-off dependent. Furthermore, in leading order in 1/e it does not have a pole, which shows that in the strong-coupling limit the electron would contribute mostly as a virtual particle to physical processes. The introduction of fermion loops would not correspond to higher orders in 1/e, so a priori our results are only pertinent to the sector of QED we have chosen. However, we present arguments showing that the previous conclusions should also apply when all the fermion loops are included.