One-particle operator representation over two-particle basis sets for relativistic QED computations

TL;DR

This paper develops a method to construct one-particle operators within a two-particle basis for relativistic QED calculations, improving accuracy and convergence in high-precision atomic computations.

Contribution

It introduces a new approach to represent one-particle operators over a many-particle basis, accounting for the full Hilbert space beyond antisymmetric subspaces.

Findings

Enables accurate computation of QED corrections in relativistic systems.

Improves convergence of interaction energy calculations.

Applicable to high-Z helium-like systems.

Abstract

This work is concerned with two-spin-1/2-fermion relativistic quantum mechanics, and it is about the construction of one-particle projectors using an inherently two(many)-particle, `explicitly correlated' basis representation, necessary for good numerical convergence of the interaction energy. It is demonstrated that a faithful representation of the one-particle operators, which appear in intermediate but essential computational steps, can be constructed over a many-particle basis set by accounting for the full Hilbert space beyond the physically relevant anti-symmetric subspace. Applications of this development can be foreseen for the computation of quantum-electrodynamics corrections for a correlated relativistic reference state and high-precision relativistic computations of medium-to-high-$Z$ helium-like systems, for which other two-particle projection techniques are unreliable.