Modular wedge localization, Majorana fields and the Tsirelson limit of the Bell-CHSH inequality

TL;DR

This paper explores how the violation of the Bell-CHSH inequality in relativistic quantum field theory can be analyzed using modular localization of Majorana fields, approaching the Tsirelson bound through spectral weight concentration.

Contribution

It provides an explicit realization of modular localization for Majorana fields and links spectral weights to Bell inequality violations in a relativistic setting.

Findings

Bell-CHSH violation approaches Tsirelson bound as spectral weight concentrates near zero.

Explicit modular localization construction for Majorana fields in 1+1 dimensions.

Vacuum correlators can be reduced to a single spectral weight function.

Abstract

The massive Majorana field in $1+1$ dimension is employed to investigate the violation of the Bell-CHSH inequality in relativistic Quantum Field Theory. We give an explicit rapidity-space realization of the Summers-Werner modular-localization construction and reduce the vacuum Bell-CHSH correlator to a single spectral weight $h^2(\omega)$ for the modular operator. The resulting analytic families approach the Tsirelson bound in the vacuum state as their spectral weight concentrates near $\omega\approx0$, corresponding to the eigenvalue $\lambda^2 \approx 1$ of the modular operator.