 The anti-ghost is taken to be a Lorentz scalar for the sake of Poincaré invariance in formula_59.However, its (anti-)commutation law relative to "c"—i.e., its quantization prescription, which ignores the spin–statistics theorem by giving Fermi–Dirac statistics to a spin-0 particle—will be given by the requirement that the inner product on our Fock space of asymptotic states be singular along directions corresponding to the raising and lowering operators of some combination of non-BRST-closed and BRST-exact fields.