Quantization Yielding Sharp and Unsharp Observables.
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| Title: | Quantization Yielding Sharp and Unsharp Observables. |
|---|---|
| Authors: | Hutagalung, Richard Tao Roni1 (AUTHOR), Hermanto, Arief1 (AUTHOR), Rosyid, Muhammad Farchani1 (AUTHOR) farchani@ugm.ac.id |
| Source: | Modern Physics Letters A. 2/28/2026, Vol. 41 Issue 6, p1-27. 27p. |
| Subjects: | Quantization (Physics), Geometric quantization, Hilbert space, Spectral theory, Hermitian operators |
| Abstract: | The so-called spectral decomposition quantization (SDQ) involving spectral decompositions of the identity operator has been proposed. The quantization yields the standard (sharp) quantum observables in the form of Hermitian operators acting in the Hilbert space of square-integrable functions. Here, the quantizable classical observables are limited as in the case of geometric quantization (GQ). It has been shown that this quantization leads to the same results as those yielded by geometric quantization in the position representation as well as in the momentum representation. The method of quantization also has been formulated in the representation concerning any pair of canonical observables. Then, the quantization has been generalized by replacing the spectral measure appearing in the spectral decompositions of the identity operator with positive-operator-valued measure constructed by using suitable smearing function (e.g. confidence distribution) so that the quantization yields unsharp quantum observables. It has been shown that the unsharp quantum observables are yielded from the quantization of the so-called unsharp quantizable classical observables. Some properties of unsharp classical observables have been investigated. The explicit expressions of unsharp quantum observables have been obtained. [ABSTRACT FROM AUTHOR] |
| Copyright of Modern Physics Letters A is the property of World Scientific Publishing Company 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 |
| FullText | Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 191138755 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Quantization Yielding Sharp and Unsharp Observables. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Hutagalung%2C+Richard+Tao+Roni%22">Hutagalung, Richard Tao Roni</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Hermanto%2C+Arief%22">Hermanto, Arief</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Rosyid%2C+Muhammad+Farchani%22">Rosyid, Muhammad Farchani</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> farchani@ugm.ac.id</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Modern+Physics+Letters+A%22">Modern Physics Letters A</searchLink>. 2/28/2026, Vol. 41 Issue 6, p1-27. 27p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Quantization+%28Physics%29%22">Quantization (Physics)</searchLink><br /><searchLink fieldCode="DE" term="%22Geometric+quantization%22">Geometric quantization</searchLink><br /><searchLink fieldCode="DE" term="%22Hilbert+space%22">Hilbert space</searchLink><br /><searchLink fieldCode="DE" term="%22Spectral+theory%22">Spectral theory</searchLink><br /><searchLink fieldCode="DE" term="%22Hermitian+operators%22">Hermitian operators</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: The so-called spectral decomposition quantization (SDQ) involving spectral decompositions of the identity operator has been proposed. The quantization yields the standard (sharp) quantum observables in the form of Hermitian operators acting in the Hilbert space of square-integrable functions. Here, the quantizable classical observables are limited as in the case of geometric quantization (GQ). It has been shown that this quantization leads to the same results as those yielded by geometric quantization in the position representation as well as in the momentum representation. The method of quantization also has been formulated in the representation concerning any pair of canonical observables. Then, the quantization has been generalized by replacing the spectral measure appearing in the spectral decompositions of the identity operator with positive-operator-valued measure constructed by using suitable smearing function (e.g. confidence distribution) so that the quantization yields unsharp quantum observables. It has been shown that the unsharp quantum observables are yielded from the quantization of the so-called unsharp quantizable classical observables. Some properties of unsharp classical observables have been investigated. The explicit expressions of unsharp quantum observables have been obtained. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Modern Physics Letters A is the property of World Scientific Publishing Company 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: 10.1142/S021773232650015X Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 27 StartPage: 1 Subjects: – SubjectFull: Quantization (Physics) Type: general – SubjectFull: Geometric quantization Type: general – SubjectFull: Hilbert space Type: general – SubjectFull: Spectral theory Type: general – SubjectFull: Hermitian operators Type: general Titles: – TitleFull: Quantization Yielding Sharp and Unsharp Observables. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Hutagalung, Richard Tao Roni – PersonEntity: Name: NameFull: Hermanto, Arief – PersonEntity: Name: NameFull: Rosyid, Muhammad Farchani IsPartOfRelationships: – BibEntity: Dates: – D: 28 M: 02 Text: 2/28/2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 02177323 Numbering: – Type: volume Value: 41 – Type: issue Value: 6 Titles: – TitleFull: Modern Physics Letters A Type: main |
| ResultId | 1 |
