Resummation of Quantum Radiation Reaction in Plane Waves.

Greger Torgrimsson

doi:10.1103/physrevlett.127.111602

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 O(α^{n}) term from O(α^{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 α expansion.

Highlights

An electron in an electromagnetic field emits photons and the recoil it experiences is called radiation reaction (RR) [1,2]
The standard equation is the Abraham-Lorentz-Dirac (LAD) equation, but since it leads to unphysical solutions it is common to replace it with the Landau-Lifshitz (LL) equation, which is free from such unphysical solutions
Since preacceleration occurs on timescales that are within the quantum regime, and since the LAD and LL equations agree quite well within the classical regime, it is common to view the LL equation as giving a correct description for practical purposes

Summary

Greger Torgrimsson *

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. In this Letter we propose a new method for obtaining quantum RR in high-intensity lasers It too is based on incoherent products of OðαÞ terms. OðαnÞ probabilities to leading order for long pulses or large a0 1⁄4 E=ω by multiplying OðαÞ Mueller matrices In this case we need MC for (nonlinear) Compton scattering and ML for the cross term between the Oðα0Þ and OðαÞ parts of the amplitude for e− → e−. To use these methods to obtain RR we need a way to evaluate all the relevant higher-order diagrams and to resum them Both photon emissions and loops [30]. More details of this derivation can be found in the Supplemental

Published by the American Physical Society

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