Field-Theoretic Weyl Deformation Quantization of Enlarged Poisson Algebras
C*-algebraic Weyl quantization is extended by allowing also degenerate pre-symplectic forms for the Weyl relations with infinitely many degrees of freedom, and by starting out from enlarged classical Poisson algebras. A powerful tool is found in the construction of Poisson algebras and non-commutati...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2008 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2008
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/149035 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Field-Theoretic Weyl Deformation Quantization of Enlarged Poisson Algebras / R. Honegger, A. Rieckers, L. Schlafer // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 61 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862710731896520704 |
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| author | Honegger, R. Rieckers, A. Schlafer, L. |
| author_facet | Honegger, R. Rieckers, A. Schlafer, L. |
| citation_txt | Field-Theoretic Weyl Deformation Quantization of Enlarged Poisson Algebras / R. Honegger, A. Rieckers, L. Schlafer // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 61 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | C*-algebraic Weyl quantization is extended by allowing also degenerate pre-symplectic forms for the Weyl relations with infinitely many degrees of freedom, and by starting out from enlarged classical Poisson algebras. A powerful tool is found in the construction of Poisson algebras and non-commutative twisted Banach-*-algebras on the stage of measures on the not locally compact test function space. Already within this frame strict deformation quantization is obtained, but in terms of Banach-*-algebras instead of C*-algebras. Fourier transformation and representation theory of the measure Banach-*-algebras are combined with the theory of continuous projective group representations to arrive at the genuine C*-algebraic strict deformation quantization in the sense of Rieffel and Landsman. Weyl quantization is recognized to depend in the first step functorially on the (in general) infinite dimensional, pre-symplectic test function space; but in the second step one has to select a family of representations, indexed by the deformation parameter h. The latter ambiguity is in the present investigation connected with the choice of a folium of states, a structure, which does not necessarily require a Hilbert space representation.
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| first_indexed | 2025-12-07T17:26:24Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-149035 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T17:26:24Z |
| publishDate | 2008 |
| publisher | Інститут математики НАН України |
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| spelling | Honegger, R. Rieckers, A. Schlafer, L. 2019-02-19T13:11:12Z 2019-02-19T13:11:12Z 2008 Field-Theoretic Weyl Deformation Quantization of Enlarged Poisson Algebras / R. Honegger, A. Rieckers, L. Schlafer // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 61 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 46L65; 47L90; 81R15 https://nasplib.isofts.kiev.ua/handle/123456789/149035 C*-algebraic Weyl quantization is extended by allowing also degenerate pre-symplectic forms for the Weyl relations with infinitely many degrees of freedom, and by starting out from enlarged classical Poisson algebras. A powerful tool is found in the construction of Poisson algebras and non-commutative twisted Banach-*-algebras on the stage of measures on the not locally compact test function space. Already within this frame strict deformation quantization is obtained, but in terms of Banach-*-algebras instead of C*-algebras. Fourier transformation and representation theory of the measure Banach-*-algebras are combined with the theory of continuous projective group representations to arrive at the genuine C*-algebraic strict deformation quantization in the sense of Rieffel and Landsman. Weyl quantization is recognized to depend in the first step functorially on the (in general) infinite dimensional, pre-symplectic test function space; but in the second step one has to select a family of representations, indexed by the deformation parameter h. The latter ambiguity is in the present investigation connected with the choice of a folium of states, a structure, which does not necessarily require a Hilbert space representation. This paper is a contribution to the Special Issue on Deformation Quantization. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Field-Theoretic Weyl Deformation Quantization of Enlarged Poisson Algebras Article published earlier |
| spellingShingle | Field-Theoretic Weyl Deformation Quantization of Enlarged Poisson Algebras Honegger, R. Rieckers, A. Schlafer, L. |
| title | Field-Theoretic Weyl Deformation Quantization of Enlarged Poisson Algebras |
| title_full | Field-Theoretic Weyl Deformation Quantization of Enlarged Poisson Algebras |
| title_fullStr | Field-Theoretic Weyl Deformation Quantization of Enlarged Poisson Algebras |
| title_full_unstemmed | Field-Theoretic Weyl Deformation Quantization of Enlarged Poisson Algebras |
| title_short | Field-Theoretic Weyl Deformation Quantization of Enlarged Poisson Algebras |
| title_sort | field-theoretic weyl deformation quantization of enlarged poisson algebras |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/149035 |
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