Stability of relativistic quantum electrodynamics in the Coulomb gauge

Abstract

We show that relativistic quantum electrodynamics in the Coulomb gauge satisfies the following bound, which establishes stability: let $H(\Lambda ,V)$ denote the Hamiltonian of $QE{D}_{1+3}$ on the three-dimensional torus of volume $V$ and with ultraviolet cutoff $\Lambda$. Then there exists a constant $0<\mu (\Lambda ,V)<\infty$ (the vacuum energy renormalization) such that the renormalized Hamiltonian is positive: $H_{ren}(\Lambda ,V)\equiv H_{\Lambda ,V}+{\mu }_{\Lambda ,V}\cdot 1\ge 0$.

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