Ghost Number Conservation I've been reading about gauge theory quantization, and understand it mostly. The only thing I don't get is why people talk about "ghost number conservation".
As far as I can tell, the ghost number is a quantity defined to be $+1$ for ghost and $-1$ for antighost fields. It is then claimed that total ghost number is conserved for the action. I don't understand what is means for something to be "conserved for an action". I only know what it means for something to be conserved in classical or quantum evolution. Alternatively I know what it means for an action to be invariant under a transformation.
Is this just bad nomenclature? I'm worried about it for the following reason. 
In the quantum theory there is a quantum "ghost number" operator which operates on the Fock space of the theory and tells you the cumulative ghosts $-$ antighosts in your state. I've seen it argued that this must commute with the Hamiltonian because "ghost number is conserved in the action". This seems pretty fundamental, but the logic seems flawed because I don't understand the terminology.
Maybe everyone just means that the ghost number is $0$, which is obvious. But this seems like too simple an explanation (why would people call it conserved, when $0$ is significantly shorter?!)
 A: "Something is conserved for an action" simply means that the action carries a zero overall value of "something" (for an additive quantity). In this case, the action has $N_{gh}=0$. It follows that the equations of motion derived from the action imply $dN_{gh}/dt=0$. Most typically, they imply $\partial_\mu J^\mu_{gh}=0$ i.e. the local continuity law for a whole current.
The action has $N_{gh}=0$ because each term contains the same number of ghost factors as antighosts. The symmetry generated by $N_{gh}$ is a $U(1)$ symmetry adding a phase $\exp(i N_{gh} \alpha)$.
We use the terminology "the ghost number is conserved" to emphasize that the ghost number generates a symmetry. The proposition "the value of the ghost number is zero" wouldn't make it clear that the quantity is measured in the same way as potentially conserved charges are measured.
The conservation applies to each term in the action (kinetic terms and interaction terms: they produce propagators and vertices in Feynman diagrams, respectively). Saying that something is zero has a different flavor in it. We usually say that something is zero when we talk about properties of a particular state or a configuration, not about properties of the action (properties of the laws of physics). The right words for the property of the laws of physics (or the action/Lagrangian) is "conserved".
Moreover, in those cases, "zero" is just another possible value. That differs from the word "conserved" which is qualitatively different from any other value that would correspond to "not conserved". 
