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We show that relativistic quantum electrodynamics in the Coulomb gaugesatisfies the following bound, which establishes stability: let $H(\Lambda,V)$denote the Hamiltonian of $QED_{1+3}$ 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 therenormalized Hamiltonian is positive: $H_{ren}(\Lambda,V) \equivH_{\Lambda,V}+\mu_{\Lambda, V}\cdot \mathbb{1} \ge 0 $.

Stability of relativistic quantum electrodynamics in the Coulomb gauge