Resummation of Quantum Radiation Reaction in Plane Waves

We propose a new approach to obtain the momentum expectation value of an electron in high-intensity laser, including multiple photon emissions and loops. find recursive formula that allows us $\mathcal{O}(\alpha^n)$ term from $\mathcal{O}(\alpha^{n-1})$, which can also be expressed as integro-differential equation. In classical limit we solution Landau-Lifshitz equation all orders. show how spin-dependent quantum radiation reaction obtained by resumming both energy expansion well $\alpha$ expansion.