On the Bottom‐Up Construction of Many‐Electron Relativistic QED Hamiltonian

ABSTRACT It was shown more than a decade ago [J. Chem. Phys. 139, 014108 (2013)] that a many‐electron relativistic quantum electrodynamics (QED) Hamiltonian for high‐precision electronic structure calculations can be constructed in a bottom‐up fashion, by virtue of charge‐conjugated contraction (CCC) of fermion operators when normal‐ordering the starting unbounded relativistic Hamiltonian (second‐quantized in terms of the electronic Dirac field) with respect to the filled negative‐energy Dirac sea of electrons. It is shown here that the same relativistic QED Hamiltonian can also be obtained by equal average of the two relativistic Hamiltonians resulting from the normal‐ordering of the starting unbounded relativistic Hamiltonians (second‐quantized in terms of the electronic and positronic Dirac fields, respectively) with respect to the filled negative‐energy Dirac seas of electrons and positrons, respectively, via the standard contraction of fermion operators. In essence, both procedures incorporate properly the fundamental charge‐conjugation symmetry of relativistic quantum mechanics to ensure the symmetric treatment of the electronic and positronic degrees of freedom.