  In this note I apply a theorem of Kohn to quantum oscillations in cuprates. I
show that when combined with Gell-Mann and Low theorem, there is rigorous
justification of quantum oscillations as in a Fermi liquid for cuprates. The
Gell-Man-Low theorem is not perturbative, and applies more generally as long as
the adiabatic evolution from an isolated non-degenerate state is the case.
Oscillation frequencies are identical to the non-interacting problem. Thus,
quantum oscillations protect the Fermi liquid and is in turn protected by it.
This is not to imply that other properties of the cuprates that do not have a
gap in the spectrum could not exhibit non-Fermi liquid behavior, for example,
angle resolved photoemission spectroscopy.
