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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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Дата: | 2008 |
| Автори: | , , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2008
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| Онлайн доступ: | 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 |
| Цитувати: | 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
nasplib_isofts_kiev_ua-123456789-149035 |
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dspace |
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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 |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Field-Theoretic Weyl Deformation Quantization of Enlarged Poisson Algebras |
| spellingShingle |
Field-Theoretic Weyl Deformation Quantization of Enlarged Poisson Algebras Honegger, R. Rieckers, A. Schlafer, L. |
| title_short |
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_sort |
field-theoretic weyl deformation quantization of enlarged poisson algebras |
| author |
Honegger, R. Rieckers, A. Schlafer, L. |
| author_facet |
Honegger, R. Rieckers, A. Schlafer, L. |
| publishDate |
2008 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| 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.
|
| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/149035 |
| 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. |
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2025-12-07T17:26:24Z |
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2025-12-07T17:26:24Z |
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