Classical and quantum ghosts
  The aim of these notes is to provide a self-contained review of why it is
generically a problem when a solution of a theory possesses ghost fields among
the perturbation modes. We define what a ghost field is and we show that its
presence is associated to a classical instability whenever the ghost field
interacts with standard fields. We then show that the instability is more
severe at quantum level, and that perturbative ghosts can exist only in low
energy effective theories. However, if we don't consider very ad-hoc choices,
compatibility with observational constraints implies that low energy effective
ghosts can exist only at the price of giving up Lorentz-invariance or locality
above the cut-off, in which case the cut-off has to be much lower that the
energy scales we currently probe in particle colliders. We also comment on the
possible role of extra degrees of freedom which break Lorentz-invariance
spontaneously.
