Living with spontaneously broken BRST symmetry. II. Poincaré invariance

Due to internal symmetries of its ghost sector, the Poincaré generators of the Gribov-Zwanziger (GZ) model are not unique. The model apparently has two linearly independent symmetric and conserved energy-momentum tensors. We show that these energy-momentum tensors are physically equivalent and differ by unobservable conserved currents only. There is a single physical energy-momentum operator that is invariant under all symmetries of the ghost sector, including Becchi-Rouet-Stora-Tyutin (BRST). This resolves concerns about Poincaré invariance raised by the explicit x-dependence of the BRST operator. The energy, momentum, and angular momentum of physical states are well-defined quantities that vanish for the ground state of this theory. We obtain and discuss the physical Ward identities resulting from Poincaré invariance.