📝 SummarXiv

Abstract

We examine the role of unitary transformations in enhancing violations of the Bell-CHSH inequality in relativistic quantum field theory. In quantum systems, all relevant observables can be expressed via unitary rotations of reference operators. We extend this perspective to a real massive free scalar field and to the Proca vector field in $(1+1)$ Minkowski spacetime. In two dimensions, the Proca theory carries only one degree of freedom and is known to be equivalent to the scalar theory, implying that both yield identical Bell-CHSH violations. After introducing suitable Hermitian operators, we employ Tomita-Takesaki modular theory to construct spacelike separated observables in the vacuum. We demonstrate that unitary deformations significantly increase the Bell-CHSH violation, approaching the Tsirelson bound, and we report the first explicit evaluation of such violation in a vector-field vacuum.