Modular operators construct wedge-localized one-particle vectors that produce Bell-CHSH violations ~2.3 for free scalar fields, with an outline for approaching Tsirelson's bound via modular-spectrum-aware operators.
String-localized Quantum Fields and Modular Localization
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abstract
We study free, covariant, quantum (Bose) fields that are associated with irreducible representations of the Poincar\'e group and localized in semi-infinite strings extending to spacelike infinity. Among these are fields that generate the irreducible representations of mass zero and infinite spin that are known to be incompatible with point-like localized fields. For the massive representation and the massless representations of finite helicity, all string-localized free fields can be written as an integral, along the string, of point-localized tensor or spinor fields. As a special case we discuss the string-localized vector fields associated with the point-like electromagnetic field and their relation to the axial gauge condition in the usual setting.
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2026 1verdicts
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Modular Theory and the Bell-CHSH inequality in relativistic scalar Quantum Field Theory
Modular operators construct wedge-localized one-particle vectors that produce Bell-CHSH violations ~2.3 for free scalar fields, with an outline for approaching Tsirelson's bound via modular-spectrum-aware operators.