Bound-state relativistic quantum electrodynamics: a perspective for precision physics with atoms and molecules

TL;DR

This paper reviews the relativistic QED framework and recent numerical advances for high-precision atomic and molecular spectroscopy, aiming to enhance fundamental physics tests beyond the Standard Model.

Contribution

It provides a concise overview of the relativistic QED approach and recent computational developments for precision atomic and molecular physics.

Findings

Overview of relativistic QED framework for atoms and molecules

Recent numerical methods enabling high-precision calculations

Potential applications in testing fundamental physics

Abstract

Precision physics aims to use atoms and molecules to test and develop the fundamental theory of matter, possibly beyond the Standard Model. Most of the atomic and molecular phenomena are described by the QED (quantum electrodynamics) sector of the Standard Model. Do we have the computational tools, algorithms, and practical equations for the most possible complete computation of atoms and molecules within the QED sector? What is the fundamental equation to start with? Is it still Schr\"odinger's wave equation for molecular matter, or is there anything beyond that? This paper provides a concise overview of the relativistic QED framework and recent numerical developments targeting precision physics and spectroscopy applications with common features with the robust and successful relativistic quantum chemistry methodology.