Relativistic Lindblad description of the electron's radiative dynamics

TL;DR

The work develops a relativistic Lindblad master equation for an electron in external fields, embedding radiation reaction (RR) and vacuum fluctuations (VF) within an open-system Dirac framework via operational dynamical modeling (ODM). It stabilizes the dynamics by enforcing PES/NES exchange through Lindblad operators and employs a Foldy–Wouthuysen projection to isolate the positive-energy sector, enabling a quantum analogue of the Landau–Lifshitz equation with RR and VF effects. The authors formulate a covariant Wigner phase-space representation and derive its semiclassical limit, linking quantum corrections to $Zitterbewegung$ and noncommutative coordinates to the classical LL/Sokolov structure. The framework provides a robust platform for exploring quantum RR in ultrastrong laser fields and suggests natural extensions to multi-particle QED regimes and numerical simulations.

Abstract

An effective model for describing the relativistic quantum dynamics of a radiating electron is developed via a relativistic generalization of the Lindblad master equation. By incorporating both radiation reaction and vacuum fluctuations into the Dirac equation within an open quantum system framework, our approach captures the Zitterbewegung of the electron, ensuing noncommutativity of its effective spatial coordinates, and provides the quantum analogue of the Landau-Lifshitz (LL) classical equation of motion with radiation reaction. We develop the corresponding phase-space representation via the relativistic Wigner function and derive the semiclassical limit through a Foldy-Wouthuysen transformation. The latter elucidates the signature of quantum vacuum fluctuations in the LL equation, and shows its relationship with the corrected Sokolov equation. Our results offer a robust framework for investigating quantum radiation reaction effects in ultrastrong laser fields.