Quantum electrodynamics, high-resolution spectroscopy and fundamental constants

Recent progress in high-resolution spectroscopy has delivered us a variety of accurate optical results, which can be used for the determination of the atomic fundamental constants and for constraining their possible time variation. We present a brief overview of the results discussing in particular, the determination of the Rydberg constant, the relative atomic weight of the electron and proton, their mass ratio and the fine structure constant. Many individual results on those constants are obtained with use of quantum electrodynamics, and we discuss which sectors of QED are involved. We derive constraints on a possible time variation of the fine structure constants and m(e)/m(p).