One perspective is to say that one introduced the ghost fields into the Lagrangian to be able to write the gauge transformation determinant as a path-integral. Hence I was tempted to think of them as just some auxiliary variables introduced into the theory to make things manageable.
But then one observes that having introduced them there is now an extra global $U(1)$ symmetry - the "ghost number"
Hence hasn't one now basically added a new factor of $U(1)$ to the symmetry group of the theory? How can the symmetry of the theory depend on introduction of some auxiliary fields?
Now if one takes the point of view that the global symmetry has been enhanced then the particles should also lie in the irreducible representations of this new factor. Hence ghost number should be like a new quantum number for the particles and which has to be conserved!
But one sees that ghost field excitations are BRST exact and hence unphysical since they are $0$ in the BRST cohomology.
I am unable to conceptually reconcile the above three ideas - the first two seem to tell me that the ghost-number is a very physical thing but the last one seems to tell me that it is unphysical.
At the risk of sounding more naive - if the particles are now charged under the ghost number symmetry then shouldn't one be able to measure that in the laboratory?
Lastly this ghost number symmetry is a global/rigid $U(1)$ symmetry - can't there be a case where it is local and needs to be gauged?