Microwave spectroscopy of confined particles in Penning traps is mainly applied to magnetic dipole transitions in various contexts. The strong magnetic field of the Penning trap gives rise to significant spin orientation energies and to Zeeman splitting of lines, which can be used for precision spectroscopy of magnetic dipole transitions and the determination of magnetic moments. Prominent examples are the precision measurements of the magnetic moments (g-factors) of the free (unbound) electron, proton and their anti-particles, as well as of the bound electron by Larmor frequency measurements, and in general the application to the Zeeman splitting of levels that occurs due to the presence of magnetic field used for confinement. We will discuss these applications in detail below.
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