An overall sign in the Lagrangian does not affect the classical equations of motion. However, at the
quantum level, if we want to preserve causality by keeping the optical theorem to be valid, then the ghost
can be interpreted as a particle which propagates with negative energy, as already stated above. In other
words, in special relativity, the ghost would have a four-momentum with
. However it
would still be a timelike particle as
, whether
is negative or not. The problem
arises when this particle is coupled to some other normal particle, because in this case the
process
with
can be allowed. This means in general that
for such a theory one would expect the pair creation of ghost and normal particles out of the
vacuum. Notice that the energy is still conserved, but the energy is pumped out of the ghost
particle.
Since all the particles are coupled at least to gravity, one would think that out of the vacuum particles could be created via the decay of a couple of gravitons emitted in the vacuum into ghosts and non-ghosts particles. This process does lead to an infinite contribution unless one introduces a cutoff for the theory [145, 161], for which one can set observational constraints.
We have already seen that, for metric f (R) gravity, the kinetic operator in the FLRW background
reduces to given in Eq. (7.60
) with the perturbed action (7.80
). Since the sign of
is
determined by
, one needs to impose
in order to avoid the propagation of a ghost
mode.
http://www.livingreviews.org/lrr-2010-3 | ![]() This work is licensed under a Creative Commons License. Problems/comments to |