Dissolution of relativistic atoms into negative energy states

The problem of atomic dissolution by means of decay to the negative energy continuum is discussed. The derivation of the one-electron central-field Hamiltonian from quantum electrodynamics is made as an example. It is found that the operators that project the Coulomb interaction into positive and negative energy states of the Dirac noninteracting Hamiltonian cause the eigenstates of the atomic Hamiltonian to break up into two sets. One set is expandable in the positive energy noninteracting states, and this set propagates forward in time. The other set is expandable in terms of the negative energy noninteracting states and propagates backward in time. There is, therefore, no danger that transitions will occur from the forward propagating eigenstates into the negative continuum with continued propagation in the forward direction, regardless of the magnitude of the nuclear charge.