Stability of matter in magnetic fields.

In the presence of arbitrarily large magnetic fields, matter composed of electrons and nuclei was known to be unstable if α or Z is too large. Here we prove that matter is stable if α < 0.06 and Zα2 < 0.04. One of the remaining unsolved problems connected with the stability of matter is the inclusion of arbitrary magnetic fields. The model is a caricature of QED which invites speculations about stability of QED for large fine structure constant, α, but that is not our focus here and we refer to [1] for a discussion of these and related matters. The Hamiltonian for N electrons and K fixed nuclei of charge Ze with magnetic field B(x) = ∇ × A(x), including the field energy, ε ∫ B, is