The global dynamics for the Maxwell-Dirac system

TL;DR

This paper investigates the global existence, decay, and scattering behavior of solutions to the (1+3) dimensional Maxwell-Dirac system, employing advanced analytical techniques to handle nonlinear resonances and establish decay estimates.

Contribution

It introduces a novel combination of vector fields energy methods and space-time resonance analysis to study the Maxwell-Dirac system's long-term dynamics and phase corrections.

Findings

Established decay estimates for solutions.

Proved global existence under Lorenz gauge.

Identified explicit phase corrections due to nonlinear resonances.

Abstract

In this paper, we study the (1+3) dimensional massive Maxwell-Dirac system in the context of global existence and asymptotic behavior of solutions under the Lorenz gauge condition, as well as the modified and linear scattering phenomena for the Dirac spinor and the electromagnetic potential, respectively. We employ a vector fields energy method combined with a detailed analysis of the space-time resonance argument. This approach allows us to establish decay estimates and energy bounds crucial for proving the main theorems. Especially, we provide the explicit phase correction arising from the strong nonlinear resonances.