Quantum electrodynamics corrections to the $2P$ fine splitting in Li

We consider quantum electrodynamics (QED) corrections to the fine splitting $E(2P_{3/2}) - E(2P_{1/2})$ in the Li atom. We derive complete formulas for the $m\,\alpha^6$ and $m\,\alpha^7\,\ln\alpha$ contributions and calculate them numerically using highly optimized, explicitly correlated basis functions. The obtained results resolve disagreement between measurements and lay the foundations for investigation of QED effects in light, many-electron atoms.