  We reconsider the Lee-Wick (LW) models and compare their properties to the
properties of the models that contain purely virtual particles. We argue
against the LW premise that unstable particles can be removed from the sets of
incoming and outgoing states in scattering processes. The removal leads to a
non-Hermitian classical limit, besides clashing with the observation of the
muon. If, on the other hand, all the states are included, the LW models have a
Hamiltonian unbounded from below or negative norms. Purely virtual particles,
on the contrary, lead to a Hermitian classical limit and are absent from the
sets of incoming and outgoing states without implications on the observation of
long-lived unstable particles. We give a vademecum to summarize the properties
of most options to treat abnormal particles. We study a method to remove the LW
ghosts only partially, by saving the physical particles they contain.
Specifically, we replace a LW ghost with a certain superposition of a purely
virtual particle and an ordinary particle, and drop only the former from the
sets of the external states. The trick can be used to make the Pauli-Villars
fields consistent and observable, without sending their masses to infinity, or
to build a finite QED, by tweaking the original Lee-Wick construction. However,
it has issues with general covariance, so it cannot be applied as is to quantum
gravity, where a manifestly covariant decomposition requires the introduction
of a massive spin-2 multiplet.
