LAUSR

We show that relativistic quantum electrodynamics in the Coulomb gauge satisfies the following bound, which establishes stability: let H(Λ, V) denote the Hamiltonian of QED1+3 on the three-dimensional torus of volume V and with ultraviolet cutoff Λ. Then there exists a constant 0 < μ(Λ, V) < ∞ (the vacuum energy renormalization) such that the renormalized Hamiltonian is positive: Hren(Λ,V)≡ HΛ,V+μΛ,V⋅1≥ 0.We show that relativistic quantum electrodynamics in the Coulomb gauge satisfies the following bound, which establishes stability: let H(Λ, V) denote the Hamiltonian of QED1+3 on the three-dimensional torus of volume V and with ultraviolet cutoff Λ. Then there exists a constant 0 < μ(Λ, V) < ∞ (the vacuum energy renormalization) such that the renormalized Hamiltonian is positive: Hren(Λ,V)≡ HΛ,V+μΛ,V⋅1≥ 0.