  The plasmon frequency in standard electron gases with a parabolic
single-particle dispersion is a purely classical quantity that is not sensitive
to electron interactions or the equation of state. We demonstrate that this
canonical result no longer holds for plasmons in three-dimensional semimetals,
which can thus be used to probe many-body effects in these systems. In
particular, we show that the plasmon frequency in an external magnetic field
displays quantum oscillations, which is not the case for the electron gas.
Using the random phase approximation, results are presented for the
magnetoplasmon dispersion and the loss function in Dirac semimetals. We include
a full discussion of the loss function in a magnetic field as a function of the
direction of propagation with respect to the magnetic field direction and
discuss the transition from large magnetic fields to the low-field limit.
