Field-Theoretic Weyl Deformation Quantization of Enlarged Poisson Algebras
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
Field-Theoretic Weyl Deformation Quantization of Enlarged Poisson Algebras
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| Creator |
Honegger, R.
Rieckers, A. Schlafer, L. |
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| 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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| Date |
2019-02-19T13:11:12Z
2019-02-19T13:11:12Z 2008 |
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| Type |
Article
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| Identifier |
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 http://dspace.nbuv.gov.ua/handle/123456789/149035 |
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| Language |
en
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| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
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| Publisher |
Інститут математики НАН України
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