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arXiv · 2510.04571

Double-pair Coulomb and Breit photon correction to the correlated relativistic energy

Péter Jeszenszki·Edit Mátyus
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Abstract

The simplest, algebraic quantum-electrodynamical corrections, due to the double-negative energy subspace and instantaneous interactions, are computed to the no-pair energy of two-spin-1/2-fermion systems. Numerical results are reported for two-electron atoms with a clamped nucleus and positronium-like genuine two-particle systems. The Bethe-Salpeter equation provides the theoretical framework, and numerical methods have been developed for its equal-time time-slice. In practice, it requires solving a sixteen-component eigenvalue equation with a two-particle Dirac Hamiltonian, including the appropriate interaction. The double-pair corrections can either be included in the interaction part of the eigenvalue equation or treated as a perturbation to the no-pair Hamiltonian. The numerical results have an $\alpha$ fine-structure constant dependence that is in excellent agreement with the known $\alpha^3E_\mathrm{h}\$-order double-pair correction of non-relativistic quantum electrodynamics.

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Péter Jeszenszki, Edit Mátyus. 2025-10-06. Double-pair Coulomb and Breit photon correction to the correlated relativistic energy. https://doi.org/10.1103/dv76-8rkt

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