Searching for Bell-CHSH-Violating Bose Operators

Abstract

We construct explicit bounded wedge-local observables for Bell inequalities in a relativistic free Bose field using an exact spectral-fibre approach. The construction turns the relevant canonical pair into measurable fibre involutions and provides an operator-algebraic proof of wedge locality, self-adjointness, unitarity, and exact anticommutation. Translation-cell observables yield an explicit Bell violation with a controlled infinite-tail error, while inclusion of reflection branches produces a substantially larger violation. These results demonstrate that simple bounded local observables can expose Bell nonlocality constructively in relativistic quantum field theory and that the translation-cell result is not artifact but a strictly valid lower bound.