Unbounded Non-Commutative Integration:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht
Springer Netherlands
1985
|
| Schriftenreihe: | Mathematical Physics Studies, A Supplementary Series to Letters in Mathematical Physics
7 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | Non-commutative integration has its origin in the classical papers of Murray and von Neumann on rings of operators, and was introduced because of unsolved problems in unitary group representations and the elucidation of various aspects of quantum-mechanical formalism, together with formal calculus in such operator rings. These papers emphasized the interest in 1I -factors and pointed out the remarkable behavior and 1 algebraic structure of the set of all unbounded closed operators affiliated to such rings. The absence of power tools in functional analysis - mainly settled in their definitive form by A. Grothendieck around 1950-195- together with the pathological manipulation of algebraic operations on closed operators in Hilbert spaces, has limited ring-theory to the study of algebras of bounded operators with the main objective the difficult question of classification up to isomorphisms of factors. This material has permitted a rigorous study of discrete systems in statistical mechanics but appears to be less convincing in other domains of physics (in the algebraic approach to field theory, for example). The striking role of Hamiltonians, Schrödinger operators and Lie group invariant properties in such areas of physics disappears in the so called C*-approach |
| Beschreibung: | 1 Online-Ressource (XX, 191 p) |
| ISBN: | 9789400952317 9789401088138 |
| DOI: | 10.1007/978-94-009-5231-7 |
Internformat
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| 490 | 1 | |a Mathematical Physics Studies, A Supplementary Series to Letters in Mathematical Physics |v 7 | |
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Datensatz im Suchindex
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| id | DE-604.BV042415211 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:20:57Z |
| institution | BVB |
| isbn | 9789400952317 9789401088138 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027850704 |
| oclc_num | 863775795 |
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| owner_facet | DE-91 DE-BY-TUM DE-83 |
| physical | 1 Online-Ressource (XX, 191 p) |
| psigel | ZDB-2-PHA ZDB-2-BAE ZDB-2-PHA_Archive |
| publishDate | 1985 |
| publishDateSearch | 1985 |
| publishDateSort | 1985 |
| publisher | Springer Netherlands |
| record_format | marc |
| series | Mathematical Physics Studies, A Supplementary Series to Letters in Mathematical Physics |
| series2 | Mathematical Physics Studies, A Supplementary Series to Letters in Mathematical Physics |
| spelling | Jurzak, J. P. Verfasser aut Unbounded Non-Commutative Integration by J. P. Jurzak Dordrecht Springer Netherlands 1985 1 Online-Ressource (XX, 191 p) txt rdacontent c rdamedia cr rdacarrier Mathematical Physics Studies, A Supplementary Series to Letters in Mathematical Physics 7 Non-commutative integration has its origin in the classical papers of Murray and von Neumann on rings of operators, and was introduced because of unsolved problems in unitary group representations and the elucidation of various aspects of quantum-mechanical formalism, together with formal calculus in such operator rings. These papers emphasized the interest in 1I -factors and pointed out the remarkable behavior and 1 algebraic structure of the set of all unbounded closed operators affiliated to such rings. The absence of power tools in functional analysis - mainly settled in their definitive form by A. Grothendieck around 1950-195- together with the pathological manipulation of algebraic operations on closed operators in Hilbert spaces, has limited ring-theory to the study of algebras of bounded operators with the main objective the difficult question of classification up to isomorphisms of factors. This material has permitted a rigorous study of discrete systems in statistical mechanics but appears to be less convincing in other domains of physics (in the algebraic approach to field theory, for example). The striking role of Hamiltonians, Schrödinger operators and Lie group invariant properties in such areas of physics disappears in the so called C*-approach Physics Theoretical, Mathematical and Computational Physics Mathematical Physics Studies, A Supplementary Series to Letters in Mathematical Physics 7 (DE-604)BV000006511 7 https://doi.org/10.1007/978-94-009-5231-7 Verlag Volltext |
| spellingShingle | Jurzak, J. P. Unbounded Non-Commutative Integration Mathematical Physics Studies, A Supplementary Series to Letters in Mathematical Physics Physics Theoretical, Mathematical and Computational Physics |
| title | Unbounded Non-Commutative Integration |
| title_auth | Unbounded Non-Commutative Integration |
| title_exact_search | Unbounded Non-Commutative Integration |
| title_full | Unbounded Non-Commutative Integration by J. P. Jurzak |
| title_fullStr | Unbounded Non-Commutative Integration by J. P. Jurzak |
| title_full_unstemmed | Unbounded Non-Commutative Integration by J. P. Jurzak |
| title_short | Unbounded Non-Commutative Integration |
| title_sort | unbounded non commutative integration |
| topic | Physics Theoretical, Mathematical and Computational Physics |
| topic_facet | Physics Theoretical, Mathematical and Computational Physics |
| url | https://doi.org/10.1007/978-94-009-5231-7 |
| volume_link | (DE-604)BV000006511 |
| work_keys_str_mv | AT jurzakjp unboundednoncommutativeintegration |