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

• URL: http://arxiv.org/abs/2312.06918v2
• Date: Sat, 2 Mar 2024 21:08:40 GMT
• Title: Using Weyl operators to study Mermin's inequalities in Quantum Field Theory
• Authors: Philipe De Fabritiis, Fillipe M. Guedes, Marcelo S. Guimaraes, Itzhak Roditi, Silvio P. Sorella
• Abstract summary: We use the Tomita-Takesaki modular theory to compute the vacuum expectation value of the Mermin operator. We are able to demonstrate that Mermin's inequalities are violated when examined within the vacuum state of a scalar field theory.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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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