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We carry out a Dirac sea reinterpretation of a discretized version of theHamiltonian of quantum electrodynamics (QED), and analyze the perturbed vacuumin the continuum limit. We argue that if certain operators can be shown to bethe self-adjoint, the perturbed vacuum will have solutions that converge nicelyin this limit to states of the infinitesimal subspace of the Hilbert spacespanned by momentum eigenstates whose momenta sum to 0. This convergence allowsus to analyze what effect the perturbed vacuum has on the physical states ofthe system. We then show that the interaction and the interference between theperturbed vacuum and the physical states actually vanish in the continuumlimit, due to the fact that the states of the perturbed vacuum only live inthis vanishingly small part of the momentum space. We furthermore show thatthis allows us to remove the terms that perturb the vacuum from theHamiltonian, without changing the dynamics of the physical states, thusyielding us a well-defined Hamiltonian for the full theory of QED.

How the perturbed vacuum might be completely decoupled from all physical states, allowing for a well-defined Hamiltonian formulation of QED