Integral quantization based on the Heisenberg–Weyl group.
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| Title: | Integral quantization based on the Heisenberg–Weyl group. |
|---|---|
| Authors: | Pȩdrak, Aleksandra1 (AUTHOR) aleksandra.pedrak@ncbj.gov.pl, Góźdź, Andrzej2 (AUTHOR) andrzej.gozdz@umcs.lublin.pl, Piechocki, Włodzimierz1 (AUTHOR) wlodzimierz.piechocki@ncbj.gov.pl, Mach, Patryk3 (AUTHOR) patryk.mach@uj.edu.pl, Cieślik, Adam3 (AUTHOR) adam.cieslik@doctoral.uj.edu.pl |
| Source: | European Physical Journal C -- Particles & Fields. Jun2025, Vol. 85 Issue 6, p1-15. 15p. |
| Subjects: | Geodesic motion, General relativity (Physics), Particle motion, Harmonic oscillators, Spacetime |
| Abstract: | We develop a relativistic framework of integral quantization applied to the motion of spinless particles in the four-dimensional Minkowski spacetime. The proposed scheme is based on coherent states generated by the action of the Heisenberg–Weyl group and has been motivated by the Hamiltonian description of the geodesic motion in General Relativity. We believe that this formulation should also allow for a generalization to the motion of test particles in curved spacetimes. A key element in our construction is the use of suitably defined positive operator-valued measures. We show that this approach can be used to quantize the one-dimensional nonrelativistic harmonic oscillator, recovering the standard Hamiltonian as obtained by the canonical quantization. A direct application of our model, including a computation of transition amplitudes between states characterized by fixed positions and momenta, is postponed to a forthcoming article. [ABSTRACT FROM AUTHOR] |
| Copyright of European Physical Journal C -- Particles & Fields is the property of Springer Nature 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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| Header | DbId: egs DbLabel: Engineering Source An: 186711211 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Integral quantization based on the Heisenberg–Weyl group. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Pȩdrak%2C+Aleksandra%22">Pȩdrak, Aleksandra</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> aleksandra.pedrak@ncbj.gov.pl</i><br /><searchLink fieldCode="AR" term="%22Góźdź%2C+Andrzej%22">Góźdź, Andrzej</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> andrzej.gozdz@umcs.lublin.pl</i><br /><searchLink fieldCode="AR" term="%22Piechocki%2C+Włodzimierz%22">Piechocki, Włodzimierz</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> wlodzimierz.piechocki@ncbj.gov.pl</i><br /><searchLink fieldCode="AR" term="%22Mach%2C+Patryk%22">Mach, Patryk</searchLink><relatesTo>3</relatesTo> (AUTHOR)<i> patryk.mach@uj.edu.pl</i><br /><searchLink fieldCode="AR" term="%22Cieślik%2C+Adam%22">Cieślik, Adam</searchLink><relatesTo>3</relatesTo> (AUTHOR)<i> adam.cieslik@doctoral.uj.edu.pl</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22European+Physical+Journal+C+--+Particles+%26+Fields%22">European Physical Journal C -- Particles & Fields</searchLink>. Jun2025, Vol. 85 Issue 6, p1-15. 15p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Geodesic+motion%22">Geodesic motion</searchLink><br /><searchLink fieldCode="DE" term="%22General+relativity+%28Physics%29%22">General relativity (Physics)</searchLink><br /><searchLink fieldCode="DE" term="%22Particle+motion%22">Particle motion</searchLink><br /><searchLink fieldCode="DE" term="%22Harmonic+oscillators%22">Harmonic oscillators</searchLink><br /><searchLink fieldCode="DE" term="%22Spacetime%22">Spacetime</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: We develop a relativistic framework of integral quantization applied to the motion of spinless particles in the four-dimensional Minkowski spacetime. The proposed scheme is based on coherent states generated by the action of the Heisenberg–Weyl group and has been motivated by the Hamiltonian description of the geodesic motion in General Relativity. We believe that this formulation should also allow for a generalization to the motion of test particles in curved spacetimes. A key element in our construction is the use of suitably defined positive operator-valued measures. We show that this approach can be used to quantize the one-dimensional nonrelativistic harmonic oscillator, recovering the standard Hamiltonian as obtained by the canonical quantization. A direct application of our model, including a computation of transition amplitudes between states characterized by fixed positions and momenta, is postponed to a forthcoming article. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of European Physical Journal C -- Particles & Fields is the property of Springer Nature 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.) |
| PLink | https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=egs&AN=186711211 |
| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1140/epjc/s10052-025-14254-2 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 15 StartPage: 1 Subjects: – SubjectFull: Geodesic motion Type: general – SubjectFull: General relativity (Physics) Type: general – SubjectFull: Particle motion Type: general – SubjectFull: Harmonic oscillators Type: general – SubjectFull: Spacetime Type: general Titles: – TitleFull: Integral quantization based on the Heisenberg–Weyl group. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Pȩdrak, Aleksandra – PersonEntity: Name: NameFull: Góźdź, Andrzej – PersonEntity: Name: NameFull: Piechocki, Włodzimierz – PersonEntity: Name: NameFull: Mach, Patryk – PersonEntity: Name: NameFull: Cieślik, Adam IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 06 Text: Jun2025 Type: published Y: 2025 Identifiers: – Type: issn-print Value: 14346044 Numbering: – Type: volume Value: 85 – Type: issue Value: 6 Titles: – TitleFull: European Physical Journal C -- Particles & Fields Type: main |
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