Operators and representation theory: canonical models for algebras of operators arising in quantum mechanics
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Amsterdam
North-Holland
1988
|
| Schriftenreihe: | North-Holland mathematics studies
147 Notas de matemática (Rio de Janeiro, Brazil) no. 120 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | Historically, operator theory and representation theory both originated with the advent of quantum mechanics. The interplay between the subjects has been and still is active in a variety of areas. This volume focuses on representations of the universal enveloping algebra, covariant representations in general, and infinite-dimensional Lie algebras in particular. It also provides new applications of recent results on integrability of finite-dimensional Lie algebras. As a central theme, it is shown that a number of recent developments in operator algebras may be handled in a particularly elegant manner by the use of Lie algebras, extensions, and projective representations. In several cases, this Lie algebraic approach to questions in mathematical physics and C*-algebra theory is new; for example, the Lie algebraic treatment of the spectral theory of curved magnetic field Hamiltonians, the treatment of irrational rotation type algebras, and the Virasoro algebra. Also examined are C*-algebraic methods used (in non-traditional ways) in the study of representations of infinite-dimensional Lie algebras and their extensions, and the methods developed by A. Connes and M.A. Rieffel for the study of the Yang-Mills problem. Cutting across traditional separations between fields of specialization, the book addresses a broad audience of graduate students and researchers Includes bibliographical references (p. 285-329) and index |
| Beschreibung: | 1 Online-Ressource (viii, 337 p.) |
| ISBN: | 9780444703217 0444703217 |
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| 500 | |a Historically, operator theory and representation theory both originated with the advent of quantum mechanics. The interplay between the subjects has been and still is active in a variety of areas. This volume focuses on representations of the universal enveloping algebra, covariant representations in general, and infinite-dimensional Lie algebras in particular. It also provides new applications of recent results on integrability of finite-dimensional Lie algebras. As a central theme, it is shown that a number of recent developments in operator algebras may be handled in a particularly elegant manner by the use of Lie algebras, extensions, and projective representations. In several cases, this Lie algebraic approach to questions in mathematical physics and C*-algebra theory is new; for example, the Lie algebraic treatment of the spectral theory of curved magnetic field Hamiltonians, the treatment of irrational rotation type algebras, and the Virasoro algebra. Also examined are C*-algebraic methods used (in non-traditional ways) in the study of representations of infinite-dimensional Lie algebras and their extensions, and the methods developed by A. Connes and M.A. Rieffel for the study of the Yang-Mills problem. Cutting across traditional separations between fields of specialization, the book addresses a broad audience of graduate students and researchers | ||
| 500 | |a Includes bibliographical references (p. 285-329) and index | ||
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Datensatz im Suchindex
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| author | Jørgensen, Palle E. T. |
| author_facet | Jørgensen, Palle E. T. |
| author_role | aut |
| author_sort | Jørgensen, Palle E. T. |
| author_variant | p e t j pet petj |
| building | Verbundindex |
| bvnumber | BV042317609 |
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| ctrlnum | (ZDB-33-EBS)ocn316566721 (OCoLC)316566721 (DE-599)BVBBV042317609 |
| dewey-full | 510 512/.55 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics 512 - Algebra |
| dewey-raw | 510 512/.55 |
| dewey-search | 510 512/.55 |
| dewey-sort | 3510 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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| isbn | 9780444703217 0444703217 |
| language | English |
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| spelling | Jørgensen, Palle E. T. Verfasser aut Operators and representation theory canonical models for algebras of operators arising in quantum mechanics Palle E.T. Jorgensen Amsterdam North-Holland 1988 1 Online-Ressource (viii, 337 p.) txt rdacontent c rdamedia cr rdacarrier North-Holland mathematics studies 147 Notas de matemática (Rio de Janeiro, Brazil) no. 120 Historically, operator theory and representation theory both originated with the advent of quantum mechanics. The interplay between the subjects has been and still is active in a variety of areas. This volume focuses on representations of the universal enveloping algebra, covariant representations in general, and infinite-dimensional Lie algebras in particular. It also provides new applications of recent results on integrability of finite-dimensional Lie algebras. As a central theme, it is shown that a number of recent developments in operator algebras may be handled in a particularly elegant manner by the use of Lie algebras, extensions, and projective representations. In several cases, this Lie algebraic approach to questions in mathematical physics and C*-algebra theory is new; for example, the Lie algebraic treatment of the spectral theory of curved magnetic field Hamiltonians, the treatment of irrational rotation type algebras, and the Virasoro algebra. Also examined are C*-algebraic methods used (in non-traditional ways) in the study of representations of infinite-dimensional Lie algebras and their extensions, and the methods developed by A. Connes and M.A. Rieffel for the study of the Yang-Mills problem. Cutting across traditional separations between fields of specialization, the book addresses a broad audience of graduate students and researchers Includes bibliographical references (p. 285-329) and index Algèbres d'opérateurs Représentations d'algèbres Operator algebras fast Representations of algebras fast Operator algebras Representations of algebras Darstellungstheorie (DE-588)4148816-7 gnd rswk-swf Operatoralgebra (DE-588)4129366-6 gnd rswk-swf Operator (DE-588)4130529-2 gnd rswk-swf Operatoralgebra (DE-588)4129366-6 s Darstellungstheorie (DE-588)4148816-7 s 1\p DE-604 Operator (DE-588)4130529-2 s 2\p DE-604 http://www.sciencedirect.com/science/book/9780444703217 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Jørgensen, Palle E. T. Operators and representation theory canonical models for algebras of operators arising in quantum mechanics Algèbres d'opérateurs Représentations d'algèbres Operator algebras fast Representations of algebras fast Operator algebras Representations of algebras Darstellungstheorie (DE-588)4148816-7 gnd Operatoralgebra (DE-588)4129366-6 gnd Operator (DE-588)4130529-2 gnd |
| subject_GND | (DE-588)4148816-7 (DE-588)4129366-6 (DE-588)4130529-2 |
| title | Operators and representation theory canonical models for algebras of operators arising in quantum mechanics |
| title_auth | Operators and representation theory canonical models for algebras of operators arising in quantum mechanics |
| title_exact_search | Operators and representation theory canonical models for algebras of operators arising in quantum mechanics |
| title_full | Operators and representation theory canonical models for algebras of operators arising in quantum mechanics Palle E.T. Jorgensen |
| title_fullStr | Operators and representation theory canonical models for algebras of operators arising in quantum mechanics Palle E.T. Jorgensen |
| title_full_unstemmed | Operators and representation theory canonical models for algebras of operators arising in quantum mechanics Palle E.T. Jorgensen |
| title_short | Operators and representation theory |
| title_sort | operators and representation theory canonical models for algebras of operators arising in quantum mechanics |
| title_sub | canonical models for algebras of operators arising in quantum mechanics |
| topic | Algèbres d'opérateurs Représentations d'algèbres Operator algebras fast Representations of algebras fast Operator algebras Representations of algebras Darstellungstheorie (DE-588)4148816-7 gnd Operatoralgebra (DE-588)4129366-6 gnd Operator (DE-588)4130529-2 gnd |
| topic_facet | Algèbres d'opérateurs Représentations d'algèbres Operator algebras Representations of algebras Darstellungstheorie Operatoralgebra Operator |
| url | http://www.sciencedirect.com/science/book/9780444703217 |
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