  It has been proposed that the coherent propagation of long-lived heavy
neutrino mass eigenstates can lead to an oscillating rate of lepton number
conserving (LNC) and violating (LNV) events, as a function of the distance
between the production and displaced decay vertices. We discuss this
phenomenon, which we refer to as heavy neutrino-antineutrino oscillations, in
the framework of quantum field theory (QFT), using the formalism of external
wave packets. General formulae for the oscillation probabilities and the number
of expected events are derived and the coherence and localisation conditions
that have to be satisfied in order for neutrino-antineutrino oscillations to be
observable are discussed. The formulae are then applied to a low scale seesaw
scenario, which features two nearly mass degenerate heavy neutrinos that can be
sufficiently long lived to produce a displaced vertex when their masses are
below the $W$ boson mass. The leading and next-to-leading order oscillation
formulae for this scenario are derived. For an example parameter point used in
previous studies, the kinematics of the considered LNC/LNV processes are
simulated, to check that the coherence and localisation conditions are
satisfied. Our results show that the phenomenon of heavy neutrino-antineutrino
oscillations can indeed occur in low scale seesaw scenarios and that the
previously used leading order formulae, derived with a plane wave approach,
provide a good approximation for the considered example parameter point.
