2000/03/02 by Elliott H. Lieb, Élliott H. Lieb, Heinz Siedentop · 1 citation
Mathematics · Physics and Astronomy · #Atomic and Molecular Physics #Quantum Mechanics and Non-Hermitian Physics #Spectral Theory in Mathematical Physics #hep-th #math-ph #math.MP
paper · pdf · doi:10.1007/s002200000265
published as Commun. Math. Phys. 213, 673-683 (2000) · 11 pages, latex2e
arxiv created 2000/03/02 · openalex publication_date 2000/09/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the relativistic electron-positron field interacting with itself via the Coulomb potential defined with the physically motivated, positive, density-density quartic interaction. The more usual normal-ordered Hamiltonian differs from the bare Hamiltonian by a quadratic term and, by choosing the normal ordering in a suitable, self-consistent manner, the quadratic term can be seen to be equivalent to a renormalization of the Dirac operator. Formally, this amounts to a Bogolubov-Valatin transformation, but in reality it is non-perturbative, for it leads to an inequivalent, fine-structure dependent representation of the canonical anticommutation relations. This non-perturbative redefinition of the electron/positron states can be interpreted as a mass, wave-function and charge renormalization, among other possibilities, but the main point is that a non-perturbative definition of normal ordering might be a useful starting point for developing a consistent quantum electrodynamics.