Ongoing precision spectroscopy experiments with atoms and molecules provide low-energy tests of the Standard Model and complement high-energy tests of matter carried out in particle colliders. I focus on the quantum electrodynamics (QED) sector of the Standard Model and aim to develop its current, practical applications to atomic and molecular bound states. The highest-precision numerical results have been obtained using the so-called non-relativistic QED approach, in which the non-relativistic energy is appended with corrections of increasing orders of the α fine structure constant. The available corrections are limited to finite orders of α and its nuclear-charge-number multiple, Zα. I aim to bridge the current precision physics methodologies with the relativistic quantum chemistry practice. The former is comprehensive (up to some finite α and Zα orders) in terms of the QED theory, the latter is useful for correlated, medium-to-high-Z systems under wet-lab chemical energy resolution. The unifying theoretical framework is found through the field-theoretic Bethe–Salpeter equation and its exact equal-time variant, in which a two-(many-)particle relativistic Hamiltonian can be identified. Within this theoretical framework, high-precision computational approaches have been recently developed in my group, which deliver results consistent with nrQED established for low Z, but include partial resummation in Zα, and hence, provide automated (numerical) access to high Zα orders. I will highlight elements of our ongoing work targeting pair, retardation, and radiative corrections to the high-precision relativistic-correlated energy.
