Resummation of quantum radiation reaction in plane waves

TL;DR

This paper introduces a recursive resummation method for quantum radiation reaction in high-intensity laser-electron interactions, connecting quantum and classical results and incorporating spin effects.

Contribution

It presents a novel recursive and integro-differential approach to resum quantum radiation reaction effects, including spin dependence, in plane wave backgrounds.

Findings

Derived a recursive formula for quantum radiation reaction terms.

Connected quantum results to the classical Landau-Lifshitz equation.

Included spin effects in the resummation framework.

Abstract

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