Modifications of bundles, elliptic integrable systems, and related problems.
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| Title: | Modifications of bundles, elliptic integrable systems, and related problems. |
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| Authors: | Zotov, A. V.1,2,3 zotov@itep.ru, Smirnov, A. V.1,4 asmirnov@itep.ru |
| Source: | Theoretical & Mathematical Physics. Oct2013, Vol. 177 Issue 1, p1281-1338. 58p. |
| Subjects: | Elliptic integrals, Characteristic classes, Quantum theory, R-matrices, Painlevé equations, Elliptic curves, Duality theory (Mathematics) |
| Abstract: | We describe a construction of elliptic integrable systems based on bundles with nontrivial characteristic classes, especially attending to the bundle-modification procedure, which relates models corresponding to different characteristic classes. We discuss applications and related problems such as the Knizhnik-Zamolodchikov-Bernard equations, classical and quantum R-matrices, monopoles, spectral duality, Painlevé equations, and the classical-quantum correspondence. For an SL(N,ℂ)-bundle on an elliptic curve with nontrivial characteristic classes, we obtain equations of isomonodromy deformations. [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 | Links: – Type: pdflink Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 91826819 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Modifications of bundles, elliptic integrable systems, and related problems. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Zotov%2C+A%2E+V%2E%22">Zotov, A. V.</searchLink><relatesTo>1,2,3</relatesTo><i> zotov@itep.ru</i><br /><searchLink fieldCode="AR" term="%22Smirnov%2C+A%2E+V%2E%22">Smirnov, A. V.</searchLink><relatesTo>1,4</relatesTo><i> asmirnov@itep.ru</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Theoretical+%26+Mathematical+Physics%22">Theoretical & Mathematical Physics</searchLink>. Oct2013, Vol. 177 Issue 1, p1281-1338. 58p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Elliptic+integrals%22">Elliptic integrals</searchLink><br /><searchLink fieldCode="DE" term="%22Characteristic+classes%22">Characteristic classes</searchLink><br /><searchLink fieldCode="DE" term="%22Quantum+theory%22">Quantum theory</searchLink><br /><searchLink fieldCode="DE" term="%22R-matrices%22">R-matrices</searchLink><br /><searchLink fieldCode="DE" term="%22Painlevé+equations%22">Painlevé equations</searchLink><br /><searchLink fieldCode="DE" term="%22Elliptic+curves%22">Elliptic curves</searchLink><br /><searchLink fieldCode="DE" term="%22Duality+theory+%28Mathematics%29%22">Duality theory (Mathematics)</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: We describe a construction of elliptic integrable systems based on bundles with nontrivial characteristic classes, especially attending to the bundle-modification procedure, which relates models corresponding to different characteristic classes. We discuss applications and related problems such as the Knizhnik-Zamolodchikov-Bernard equations, classical and quantum R-matrices, monopoles, spectral duality, Painlevé equations, and the classical-quantum correspondence. For an SL(N,ℂ)-bundle on an elliptic curve with nontrivial characteristic classes, we obtain equations of isomonodromy deformations. [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: 10.1007/s11232-013-0106-1 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 58 StartPage: 1281 Subjects: – SubjectFull: Elliptic integrals Type: general – SubjectFull: Characteristic classes Type: general – SubjectFull: Quantum theory Type: general – SubjectFull: R-matrices Type: general – SubjectFull: Painlevé equations Type: general – SubjectFull: Elliptic curves Type: general – SubjectFull: Duality theory (Mathematics) Type: general Titles: – TitleFull: Modifications of bundles, elliptic integrable systems, and related problems. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Zotov, A. V. – PersonEntity: Name: NameFull: Smirnov, A. V. IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 10 Text: Oct2013 Type: published Y: 2013 Identifiers: – Type: issn-print Value: 00405779 Numbering: – Type: volume Value: 177 – Type: issue Value: 1 Titles: – TitleFull: Theoretical & Mathematical Physics Type: main |
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