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BRST invariant formulation of the Bell-CHSH inequality in gauge field theories

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arxiv 2304.01028 v2 pith:OJEHL5BH submitted 2023-04-03 hep-th hep-phquant-ph

David Dudal , Philipe De Fabritiis , Marcelo S. Guimaraes , Giovani Peruzzo , Silvio P. Sorella This is my paper · ORCID
classification hep-thhep-phquant-ph
keywords inequalitybell-chshbrstinvariantfieldgaugetheoriesabelian
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abstract

A study of the Bell-CHSH inequality in gauge field theories is presented. By using the Kugo-Ojima analysis of the BRST charge cohomology in Fock space, the Bell-CHSH inequality is formulated in a manifestly BRST invariant way. The examples of the free four-dimensional Maxwell theory and the Abelian Higgs model are scrutinized. The inequality is probed by using BRST invariant squeezed states, allowing for large Bell-CHSH inequality violations, close to Tsirelson's bound. An illustrative comparison with the entangled state of two $1/2$ spin particles in Quantum Mechanics is provided.

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