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

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.

arXiv comment12 pages. Revised version. Accepted for publication in SciPost Physics

References in corpus (28)

• Significant-loophole-free test of Bell's theorem with entangled photons
• Bell inequalities for arbitrarily high dimensional systems
• Maximal Violation of Bell's Inequalities for Continuous Variable Systems
• Entanglement and quantum tomography with top quarks at the LHC
• Quantum tops at the LHC: from entanglement to Bell inequalities
• Quantum information with top quarks in QCD
• Bell inequalities for entangled kaons and their unitary time evolution
• Improved tests of entanglement and Bell inequalities with LHC tops
• Quantum discord and steering in top quarks at the LHC
• A quantum information theoretic analysis of three flavor neutrino oscillations
• Testing entanglement and Bell inequalities in $H\to ZZ$
• Constraining new physics in entangled two-qubit systems: top-quark, tau-lepton and photon pairs
• Quantum state tomography, entanglement detection and Bell violation prospects in weak decays of massive particles
• Squeezed States in the de Sitter Vacuum
• Bell inequalities and quantum entanglement in weak gauge bosons production at the LHC and future colliders
• Measurement of Bell-type inequalities and quantum entanglement from $\Lambda$-hyperon spin correlations at high energy colliders
• Bell's Inequalities for Continuous-Variable Systems in Generic Squeezed States
• Quantum correlations in B and K meson systems
• Distillability and positivity of partial transposes in general quantum field systems
• Three-party entanglement from positronium
• Bipartite temporal Bell inequalities for two-mode squeezed states
• Maximal violation of the Bell-Clauser-Horne-Shimony-Holt inequality via bumpified Haar wavelets
• Testing Bell's Inequality using Charmonium Decays
• Bell Inequalities for Position Measurements
• Squeezed condensate of gluons and $\eta -{\eta }^{\prime }$ mass difference
• Remarks on the Clauser-Horne-Shimony-Holt inequality in relativistic quantum field theory
• On the Feynman path integral formulation of the Bell-Clauser-Horne-Shimony-Holt inequality in Quantum Field Theory
• Comments on the Bell-Clauser-Horne-Shimony-Holt inequality

Cited by in corpus (4)

• Imprints of screened dark energy on nonlocal quantum correlations
• Bell's inequality in relativistic Quantum Field Theory
• Numerical approach to the Bell-Clauser-Horne-Shimony-Holt inequality in quantum field theory
• Using Weyl operators to study Mermin's inequalities in Quantum Field Theory