Quantum Electrodynamic Corrections to Quantum Cyclotron Energy Levels*

This talk focuses on the evaluation of relativistic and quantum electrodynamic corrections to the energy levels of quantum cyclotron states. These states form the basis for the determination of fundamental constants (g factor of the electron and positron, atomic masse) in Penning traps. We have recently analyzed the relativistic corrections in detail in [Phys. Rev.A vol. 106, 012816 (2022)] on the basis of higher-order Foldy-Wouthuysen transformations. Small modifications of literature values were found. The evaluation of quantum electrodynamic corrections requires the evaluation of bound-state Feynman diagrams with up to six magnetic vertices [Phys. Rev. D vol. 108, 036004 (2023)] and the use of fully relativistic Landau levels in the symmetric gauge, which were derived in [Phys. Rev. D vol. 108, 016016 (2023)]. Apparatus-dependent effects could limit the ultimate precision of the determination of the electron g factor [Phys. Rev. D vol. 107, 076014 (2023)], with the main apparatus-dependent effects impacting the so-called axial frequency.