Poincare' Symmetry of the GZ-Model

TL;DR

This paper clarifies the Poincare' symmetry structure of the GZ-model, showing a unique physical energy-momentum operator consistent with all ghost sector symmetries, resolving invariance concerns.

Contribution

It demonstrates the physical equivalence of two energy-momentum tensors in the GZ-model and identifies a single invariant energy-momentum operator respecting all ghost sector symmetries.

Findings

Two linearly independent energy-momentum tensors are physically equivalent.

A single invariant energy-momentum operator exists for the GZ-model.

Physical quantities like energy and momentum vanish for the ground state.

Abstract

Due to internal symmetries of its ghost sector, the Poincare' generators of the 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 BRST. This resolves concerns about Poincare' 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 Poincare' invariance.