Local well-posedness for the Maxwell-Dirac system in temporal gauge

2021/06/28 by Hartmut Pecher, Pecher, Hartmut
Engineering · Mathematics · #35L70 #35Q61 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Spectral Theory in Mathematical Physics #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2106.14768

openalex publication_date 2021/06/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the low regularity well-posedness problem for the Maxwell-Dirac system in n+1 dimensions in the cases n=3 and n=2 : ∂^μ F_μν amp; = - ⟨ ψ,α_ν ψ⟩
-i α^μ ∂_μ ψamp; = A_μ α^μ ψ , where F_μν = ∂^μ A_ν - ∂^ν A_μ , and α^μ are the Dirac matrices. We assume the temporal gauge A₀=0 and make use of the fact that some of the nonlinearities fulfill a null condition. Because we work in the temporal gauge we also apply a method, which was used by Tao for the Yang-Mills system in this gauge.

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