Radiative Energy and Mass Shifts of Quantum Cyclotron States

We discuss relativistic and radiative corrections to the energies of quantum cyclotron states. In particular, it is shown analytically that the leading logarithmic radiative (self-energy) correction to the bound-state energy levels of quantum cyclotron states is state-independent, and must be interpreted as a magnetic-field-dependent correction to the electron’s mass in a Penning trap.