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 quantum
electrodynamics (QED) 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
Schrödinger’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 of the robust and successful relativistic quantum chemistry
methodology.