Maximally Superintegrable Gaudin Magnet: A Unified Approach.
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| Title: | Maximally Superintegrable Gaudin Magnet: A Unified Approach. |
|---|---|
| Authors: | Ballesteros, Á.1 angelb@ubu.es, Musso, F.2 musso@fm.sissa.it, Ragnisco, O.3 ragnisco@fis.uniroma3.it |
| Source: | Theoretical & Mathematical Physics. Dec2003, Vol. 137 Issue 3, p1645-1651. 7p. |
| Subjects: | Hamiltonian systems, Abelian equations, Poisson algebras, Hermitian operators, Differentiable dynamical systems, Linear operators |
| Abstract: | A classical integrable Hamiltonian system is defined by an Abelian subalgebra (of suitable dimension) of a Poisson algebra, while a quantum integrable Hamiltonian system is defined by an Abelian subalgebra (of suitable dimension) of a Jordan–Lie algebra of Hermitian operators. We propose a method for obtaining “large” Abelian subalgebras inside the tensor product of free tensor algebras, and we show that there exist canonical morphisms from these algebras to Poisson algebras and Jordan–Lie algebras of operators. We can thus prove the integrability of some particular Hamiltonian systems simultaneously at both the classical and the quantum level. We propose a particular case of the rational Gaudin magnet as an example. [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 |
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| Items | – Name: Title Label: Title Group: Ti Data: Maximally Superintegrable Gaudin Magnet: A Unified Approach. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Ballesteros%2C+Á%2E%22">Ballesteros, Á.</searchLink><relatesTo>1</relatesTo><i> angelb@ubu.es</i><br /><searchLink fieldCode="AR" term="%22Musso%2C+F%2E%22">Musso, F.</searchLink><relatesTo>2</relatesTo><i> musso@fm.sissa.it</i><br /><searchLink fieldCode="AR" term="%22Ragnisco%2C+O%2E%22">Ragnisco, O.</searchLink><relatesTo>3</relatesTo><i> ragnisco@fis.uniroma3.it</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Theoretical+%26+Mathematical+Physics%22">Theoretical & Mathematical Physics</searchLink>. Dec2003, Vol. 137 Issue 3, p1645-1651. 7p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Hamiltonian+systems%22">Hamiltonian systems</searchLink><br /><searchLink fieldCode="DE" term="%22Abelian+equations%22">Abelian equations</searchLink><br /><searchLink fieldCode="DE" term="%22Poisson+algebras%22">Poisson algebras</searchLink><br /><searchLink fieldCode="DE" term="%22Hermitian+operators%22">Hermitian operators</searchLink><br /><searchLink fieldCode="DE" term="%22Differentiable+dynamical+systems%22">Differentiable dynamical systems</searchLink><br /><searchLink fieldCode="DE" term="%22Linear+operators%22">Linear operators</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: A classical integrable Hamiltonian system is defined by an Abelian subalgebra (of suitable dimension) of a Poisson algebra, while a quantum integrable Hamiltonian system is defined by an Abelian subalgebra (of suitable dimension) of a Jordan–Lie algebra of Hermitian operators. We propose a method for obtaining “large” Abelian subalgebras inside the tensor product of free tensor algebras, and we show that there exist canonical morphisms from these algebras to Poisson algebras and Jordan–Lie algebras of operators. We can thus prove the integrability of some particular Hamiltonian systems simultaneously at both the classical and the quantum level. We propose a particular case of the rational Gaudin magnet as an example. [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: 10.1023/B:TAMP.0000007913.22639.d3 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 7 StartPage: 1645 Subjects: – SubjectFull: Hamiltonian systems Type: general – SubjectFull: Abelian equations Type: general – SubjectFull: Poisson algebras Type: general – SubjectFull: Hermitian operators Type: general – SubjectFull: Differentiable dynamical systems Type: general – SubjectFull: Linear operators Type: general Titles: – TitleFull: Maximally Superintegrable Gaudin Magnet: A Unified Approach. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Ballesteros, Á. – PersonEntity: Name: NameFull: Musso, F. – PersonEntity: Name: NameFull: Ragnisco, O. IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 12 Text: Dec2003 Type: published Y: 2003 Identifiers: – Type: issn-print Value: 00405779 Numbering: – Type: volume Value: 137 – Type: issue Value: 3 Titles: – TitleFull: Theoretical & Mathematical Physics Type: main |
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