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Using Weyl operators to study Mermin's inequalities in Quantum Field Theory

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arxiv 2312.06918 v2 pith:BHKTW23S submitted 2023-12-12 hep-th quant-ph

classification hep-thquant-ph
keywords mermininequalitiestheoryfieldoperatorsmodularquantumvacuum
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Mermin's inequalities are investigated in a Quantum Field Theory framework by using von Neumann algebras built with Weyl operators. We devise a general construction based on the Tomita-Takesaki modular theory and use it to compute the vacuum expectation value of the Mermin operator, analyzing the parameter space and explicitly exhibiting a violation of Mermin's inequalities. Therefore, relying on the power of modular operators, we are able to demonstrate that Mermin's inequalities are violated when examined within the vacuum state of a scalar field theory.

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