Published February 29, 2024 | Version v1
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Using Weyl operators to study Mermin's inequalities in quantum field theory

Creators

  • 1. Centro Brasileiro de Pesquisas Físicas
  • 2. Universidade do Estado do Rio de Janeiro

Description

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.

⚠️ This is an automatic machine translation with an accuracy of 90-95%

Translated Description (Arabic)

يتم التحقيق في متباينات Mermin في إطار نظرية المجال الكمومي باستخدام جبر von Neumann الذي تم إنشاؤه باستخدام مشغلي Weyl. نبتكر بنية عامة تستند إلى نظرية وحدات Tomita - Takesaki ونستخدمها لحساب قيمة توقع الفراغ لمشغل Mermin، وتحليل مساحة المعلمة وإظهار انتهاك صريح لعدم المساواة في Mermin. لذلك، بالاعتماد على قوة العوامل المعيارية، نحن قادرون على إثبات أن متباينات Mermin تنتهك عند فحصها في حالة الفراغ لنظرية المجال القياسي.

Translated Description (French)

Les inégalités de Mermin sont étudiées dans un cadre de théorie quantique des champs en utilisant des algèbres de von Neumann construites avec des opérateurs de Weyl. Nous concevons une construction générale basée sur la théorie modulaire de Tomita-Takesaki et l'utilisons pour calculer la valeur d'espérance de vide de l'opérateur Mermin, en analysant l'espace des paramètres et en présentant explicitement une violation des inégalités de Mermin. Par conséquent, en nous appuyant sur la puissance des opérateurs modulaires, nous sommes en mesure de démontrer que les inégalités de Mermin sont violées lorsqu'elles sont examinées dans l'état de vide d'une théorie du champ scalaire.

Translated Description (Spanish)

Las desigualdades de Mermin se investigan en un marco de teoría cuántica de campos mediante el uso de álgebras de von Neumann construidas con operadores de Weyl. Diseñamos una construcción general basada en la teoría modular Tomita-Takesaki y la utilizamos para calcular el valor de expectativa de vacío del operador Mermin, analizando el espacio de parámetros y mostrando explícitamente una violación de las desigualdades de Mermin. Por lo tanto, confiando en el poder de los operadores modulares, podemos demostrar que las desigualdades de Mermin se violan cuando se examinan dentro del estado de vacío de una teoría de campos escalar.

Files

PhysRevD.109.045020.pdf

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Additional details

Additional titles

Translated title (Arabic)
استخدام مشغلي Weyl لدراسة متباينات Mermin في نظرية المجال الكمومي
Translated title (French)
Utilisation des opérateurs de Weyl pour étudier les inégalités de Mermin en théorie quantique des champs
Translated title (Spanish)
Usar operadores de Weyl para estudiar las desigualdades de Mermin en la teoría cuántica de campos

Identifiers

Other
https://openalex.org/W4392296860
DOI
10.1103/physrevd.109.045020

Is supplement to
https://openalex.org/W3114678873 (Other)
https://openalex.org/W2792499845 (Other)
https://openalex.org/W2053780337 (Other)
https://openalex.org/W2053753759 (Other)
https://openalex.org/W2027451898 (Other)
https://openalex.org/W2026443688 (Other)
https://openalex.org/W2016323026 (Other)
https://openalex.org/W2010647687 (Other)
https://openalex.org/W1974180739 (Other)
https://openalex.org/W1930008428 (Other)

GreSIS Basics Section

Is Global South Knowledge
Yes
Country
Brazil

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