  Cyclotron resonance in graphene is studied with focus on many-body
corrections to the resonance energies, which evade Kohn's theorem. The genuine
many-body corrections turn out to derive from vacuum polarization, specific to
graphene, which diverges at short wavelengths. Special emphasis is placed on
the need for renormalization, which allows one to determine many-body
corrections uniquely from one resonance to another. For bilayer graphene, in
particular, both intralayer and interlayer coupling strengths undergo infinite
renormalization; as a result, the renormalized velocity and interlayer coupling
strength run with the magnetic field. A comparison of theory with the
experimental data is made for both monolayer and bilayer graphene.
