We all know Faddeev-Popov ghosts are needed in manifestly Lorentz covariant nonabelian quantum gauge theories. We also all know they decouple from the rest of matter asymptotically, although they "superficially" interact over finite time periods.
So, what is their ontological status?
If they don't really exist, can we just formulate a local theory without them?
OK, we can using spin foams?
So are they not really needed?
If they do "exist" out there, then say a state with an electron and no ghosts is "actually" different in "reality" from the state with same electron with the same momentum, but with a ghost added?
According to the formalism, they are different states. But observationally, we can never tell the difference. Both states will always give the same observable results for any physical observation. So are they the same state or not?
Do we just take the partial trace over the ghost sector?
But that's not gauge invariant except asymptotically, is it?