Model P(φ)4 quantum field theory. A nonstandard approach based on nonstandard pointwise-defined quantum fields. The field operators and the approximate vacuum.
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| Title: | Model P(φ) |
|---|---|
| Authors: | Foukzon, Jaykov1 jaikovfoukzon@gmail.com |
| Source: | Physics Essays. Mar2026, Vol. 39 Issue 1, p53-87. 35p. |
| Subjects: | Quantum field theory, Operator functions, Vacuum energy (Astronomy), Lorentz invariance, C*-algebras |
| Abstract (English): | A new non-Archimedean approach to interacting quantum fields is presented. In the proposed approach, a field operator φ(x, t) is no longer a standard tempered operator-valued distribution but a nonclassical operator-valued function. We prove using this novel approach that a quantum field theory with a Hamiltonian P(φ)4 exists and that the corresponding C*-algebra of bounded observables satisfies all the Haag-Kastler axioms except for the Lorentz covariance. We prove that the λ(φ4)4 quantum field theory model is Lorentz covariant. In this paper, we consider a somewhat different hyperfinite cutoff theory, namely, the λ: φ44: theory in a periodic box. This gives a cutoff interaction that is translation invariant, and therefore, it is useful for the study of the vacuum state. In a hyperfinite interval, we prove that the total Hamiltonian is self-#-adjoint and has a complete set of normalizable eigenstates. [ABSTRACT FROM AUTHOR] |
| Abstract (French): | Une nouvelle approche non archimédienne des champs quantiques en interaction est présentée. Dans l'approche proposée, un opérateur de champ (x,t) n'est plus une distribution à valeurs d'opérateur tempérée standard, mais une fonction à valeurs d'opérateur non classique. Nous prouvons, grâce à cette nouvelle approche, que la théorie quantique des champs avec l'hamiltonien P(), existe et que l'algèbre C* correspondante d'observables bornées satisfait tous les axiomes de Haag-Kastler, à l'exception de la covariance de Lorentz. Nous prouvons que le modèle de théorie quantique des champs (4), est covariant de Lorentz. Dans cet article, nous considérons une théorie de coupure hyperfinie quelque peu différente, savoir la théorie (4) dans une boîte périodique. Cela donne une interaction de coupure invariante par translation, et donc utile pour l'étude de l'état du vide. Dans un intervalle hyperfini, nous prouvons que l'hamiltonien total est #-adjoint et possède un ensemble complet d'états propres normalisables. [ABSTRACT FROM AUTHOR] |
| Copyright of Physics Essays is the property of Physics Essays Publication and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
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| Items | – Name: Title Label: Title Group: Ti Data: Model P(φ)<subscript>4</subscript> quantum field theory. A nonstandard approach based on nonstandard pointwise-defined quantum fields. The field operators and the approximate vacuum. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Foukzon%2C+Jaykov%22">Foukzon, Jaykov</searchLink><relatesTo>1</relatesTo><i> jaikovfoukzon@gmail.com</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Physics+Essays%22">Physics Essays</searchLink>. Mar2026, Vol. 39 Issue 1, p53-87. 35p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Quantum+field+theory%22">Quantum field theory</searchLink><br /><searchLink fieldCode="DE" term="%22Operator+functions%22">Operator functions</searchLink><br /><searchLink fieldCode="DE" term="%22Vacuum+energy+%28Astronomy%29%22">Vacuum energy (Astronomy)</searchLink><br /><searchLink fieldCode="DE" term="%22Lorentz+invariance%22">Lorentz invariance</searchLink><br /><searchLink fieldCode="DE" term="%22C*-algebras%22">C*-algebras</searchLink> – Name: Abstract Label: Abstract (English) Group: Ab Data: A new non-Archimedean approach to interacting quantum fields is presented. In the proposed approach, a field operator φ(x, t) is no longer a standard tempered operator-valued distribution but a nonclassical operator-valued function. We prove using this novel approach that a quantum field theory with a Hamiltonian P(φ)4 exists and that the corresponding C*-algebra of bounded observables satisfies all the Haag-Kastler axioms except for the Lorentz covariance. We prove that the λ(φ4)4 quantum field theory model is Lorentz covariant. In this paper, we consider a somewhat different hyperfinite cutoff theory, namely, the λ: φ44: theory in a periodic box. This gives a cutoff interaction that is translation invariant, and therefore, it is useful for the study of the vacuum state. In a hyperfinite interval, we prove that the total Hamiltonian is self-#-adjoint and has a complete set of normalizable eigenstates. [ABSTRACT FROM AUTHOR] – Name: Abstract Label: Abstract (French) Group: Ab Data: Une nouvelle approche non archimédienne des champs quantiques en interaction est présentée. Dans l'approche proposée, un opérateur de champ (x,t) n'est plus une distribution à valeurs d'opérateur tempérée standard, mais une fonction à valeurs d'opérateur non classique. Nous prouvons, grâce à cette nouvelle approche, que la théorie quantique des champs avec l'hamiltonien P(), existe et que l'algèbre C* correspondante d'observables bornées satisfait tous les axiomes de Haag-Kastler, à l'exception de la covariance de Lorentz. Nous prouvons que le modèle de théorie quantique des champs (4), est covariant de Lorentz. Dans cet article, nous considérons une théorie de coupure hyperfinie quelque peu différente, savoir la théorie (4) dans une boîte périodique. Cela donne une interaction de coupure invariante par translation, et donc utile pour l'étude de l'état du vide. Dans un intervalle hyperfini, nous prouvons que l'hamiltonien total est #-adjoint et possède un ensemble complet d'états propres normalisables. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Physics Essays is the property of Physics Essays Publication and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.4006/0836-1398-39.1.053 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 35 StartPage: 53 Subjects: – SubjectFull: Quantum field theory Type: general – SubjectFull: Operator functions Type: general – SubjectFull: Vacuum energy (Astronomy) Type: general – SubjectFull: Lorentz invariance Type: general – SubjectFull: C*-algebras Type: general Titles: – TitleFull: Model P(φ)4 quantum field theory. A nonstandard approach based on nonstandard pointwise-defined quantum fields. The field operators and the approximate vacuum. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Foukzon, Jaykov IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 03 Text: Mar2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 08361398 Numbering: – Type: volume Value: 39 – Type: issue Value: 1 Titles: – TitleFull: Physics Essays Type: main |
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