Point particles as spin chains.
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| Title: | Point particles as spin chains. |
|---|---|
| Authors: | Krivorol, V. A.1,2 (AUTHOR) v.a.krivorol@gmail.com |
| Source: | Theoretical & Mathematical Physics. Jun2026, Vol. 227 Issue 3, p1038-1052. 15p. |
| Subjects: | Geometric quantization, Quantum spin models, Submanifolds, Particle physics, Riemannian manifolds, Hamiltonian mechanics, Laplacian operator |
| Abstract: | This work surveys a recently developed approach to the study of free point particles on Riemannian manifolds, based on the Kirillov orbit method, geometric quantization, and the geometry of Lagrangian submanifolds. We show that, given a Lagrangian submanifold embedded in a product of coadjoint orbits and a Hamiltonian attaining its minimum on this submanifold, such a configuration naturally induces free point particle dynamics on. The metric governing this dynamics is precisely defined by the quadratic expansion of around its minimum. Upon quantization, this correspondence establishes a relation between and a corresponding spin-chain Hilbert space as well as a spectral equivalence between the Laplace–Beltrami operator on and a spin Hamiltonian. Explicit examples of this construction are presented for particles moving on the complex plane, two-dimensional sphere, flag manifolds, and the hyperbolic plane. [ABSTRACT FROM AUTHOR] |
| Copyright of Theoretical & Mathematical Physics 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 |
| FullText | Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 194868587 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Point particles as spin chains. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Krivorol%2C+V%2E+A%2E%22">Krivorol, V. A.</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<i> v.a.krivorol@gmail.com</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Theoretical+%26+Mathematical+Physics%22">Theoretical & Mathematical Physics</searchLink>. Jun2026, Vol. 227 Issue 3, p1038-1052. 15p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Geometric+quantization%22">Geometric quantization</searchLink><br /><searchLink fieldCode="DE" term="%22Quantum+spin+models%22">Quantum spin models</searchLink><br /><searchLink fieldCode="DE" term="%22Submanifolds%22">Submanifolds</searchLink><br /><searchLink fieldCode="DE" term="%22Particle+physics%22">Particle physics</searchLink><br /><searchLink fieldCode="DE" term="%22Riemannian+manifolds%22">Riemannian manifolds</searchLink><br /><searchLink fieldCode="DE" term="%22Hamiltonian+mechanics%22">Hamiltonian mechanics</searchLink><br /><searchLink fieldCode="DE" term="%22Laplacian+operator%22">Laplacian operator</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: This work surveys a recently developed approach to the study of free point particles on Riemannian manifolds, based on the Kirillov orbit method, geometric quantization, and the geometry of Lagrangian submanifolds. We show that, given a Lagrangian submanifold embedded in a product of coadjoint orbits and a Hamiltonian attaining its minimum on this submanifold, such a configuration naturally induces free point particle dynamics on. The metric governing this dynamics is precisely defined by the quadratic expansion of around its minimum. Upon quantization, this correspondence establishes a relation between and a corresponding spin-chain Hilbert space as well as a spectral equivalence between the Laplace–Beltrami operator on and a spin Hamiltonian. Explicit examples of this construction are presented for particles moving on the complex plane, two-dimensional sphere, flag manifolds, and the hyperbolic plane. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Theoretical & Mathematical Physics 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.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1134/S0040577926060103 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 15 StartPage: 1038 Subjects: – SubjectFull: Geometric quantization Type: general – SubjectFull: Quantum spin models Type: general – SubjectFull: Submanifolds Type: general – SubjectFull: Particle physics Type: general – SubjectFull: Riemannian manifolds Type: general – SubjectFull: Hamiltonian mechanics Type: general – SubjectFull: Laplacian operator Type: general Titles: – TitleFull: Point particles as spin chains. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Krivorol, V. A. IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 06 Text: Jun2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 00405779 Numbering: – Type: volume Value: 227 – Type: issue Value: 3 Titles: – TitleFull: Theoretical & Mathematical Physics Type: main |
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