emphasized textIn this contribution, we discuss the theory of the bound-electron g factor. This quantity can be measured nowadays to high precision in Penning-trap setups. The collaboration of theory and experiment enables impactful and detailed tests of quantum electrodynamics in a strong background electric field, and a competitive determination of fundamental constants  and nuclear properties . Very recently, we have shown that such studies also allow to test certain extensions of the standard model of particle physics : in study addressing the isotope shift of the g factor of H-like Ne ions, a competitive bound was set on the strength of a hypothetical fifth force by combining the experimental value of the isotope shift with the precision theory of nuclear recoil within QED.
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