Field-Theoretic Weyl Deformation Quantization of Enlarged Poisson Algebras
| dc.creator | Honegger, Reinhard | |
| dc.creator | Rieckers, Alfred | |
| dc.creator | Schlafer, Lothar | |
| dc.date | 2008-05-29 | |
| dc.date.accessioned | 2026-07-07T12:20:04Z | |
| dc.date.available | 2026-07-07T12:20:04Z | |
| dc.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 $\hbar$. 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. | |
| dc.description | This is a contribution to the Special Issue on Deformation Quantization, published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/ | |
| dc.identifier | https://arxiv.org/abs/0805.4536 | |
| dc.identifier | http://arxiv.org/abs/0805.4536 | |
| dc.identifier | SIGMA 4:047,2008 | |
| dc.identifier | doi:10.3842/SIGMA.2008.047 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/212966 | |
| dc.subject | Mathematical Physics | |
| dc.subject | High Energy Physics - Theory | |
| dc.subject | Quantum Algebra | |
| dc.title | Field-Theoretic Weyl Deformation Quantization of Enlarged Poisson Algebras | |
| dc.type | text |