Answer by Qmechanic for Why are physical states not eigenstates of BRST charge?
For starters, the BRST charge operator is Grassmann-odd, so an eigenvalue would be Grassmann-odd as well, which is unphysical.
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In many texts in quantum field theory or string theory, it is stated that the BRST charge $Q$ must annihilate physical states because the states are required to be BRST invariant. Since $Q$ generates...
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