We evaluate a non-perturbative QED contribution to the electron g-2 which comes from virtual positronium. We find it to be 9.0*10^{-14}. This value is comparable to the five-loop contribution of usual perturbative calculation, and several times larger than the electroweak correction.
Cite
@article{arxiv.1311.7109,
title = {Bound State Effect on the Electron g-2},
author = {Go Mishima},
journal= {arXiv preprint arXiv:1311.7109},
year = {2013}
}