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

TL;DR

This paper constructs Hermitian dichotomic operators in relativistic scalar Quantum Field Theory using vacuum projectors and Weyl operators, demonstrating violations of Bell and Mermin inequalities through numerical analysis.

Contribution

It introduces a novel method to analyze Bell and Mermin inequalities in Quantum Field Theory using vacuum projectors and Weyl operators with numerical validation.

Findings

Significant violations of Bell inequalities observed.

Mermin inequalities also violated in the quantum field context.

Cluster property checked and confirmed.

Abstract

The use of the vacuum projector $|0 \rangle \langle 0| $ 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.