Bell and Mermin inequalities in Quantum Field Theory from vacuum projectors and Weyl operators

The use of the vacuum projector $\mathrm{\mid }0⟩⟨0\mathrm{\mid }$ and of the unitary Weyl operators enables us to construct a set of Hermitian dichotomic operators in relativistic scalar Quantum Field Theory in Minkowski spacetime. Employing test functions supported in diamond regions, both Bell and Mermin inequalities are studied by means of a numerical setup. In addition to reporting expressive violations of both inequalities, the cluster property is also checked.