The effects of electron-electron interactions on cyclotron resonance frequency are analyzed on the basis of the Fermi liquid theory. In Galilean invariant systems the cyclotron resonance frequency is independent of electron-electron interactions (Kohn's theorem). This theorem is due to the backflow effect by which the momentum conservation law is recovered. Umklapp processes tend to reduce the resonance frequency from the cyclotron frequency of non-interacting electrons.
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Kanki et al. (1997) studied this question.