Matrixvalued BerezinToeplitz quantization
Abstract
We generalize some earlier results on a BerezinToeplitz type of quantization on Hilbert spaces built over certain matrix domains. In the present, wider setting, the theory could be applied to systems possessing several kinematic and internal degrees of freedom. Our analysis leads to an identification of those observables, in this general context, which admit a semiclassical limit and those for which no such limit exists. It turns out that the latter class of observables involves the internal degrees of freedom in an intrinsic way. Mathematically, the theory, being a generalization of the standard BerezinToeplitz quantization, points the way to applying such a quantization technique to possibly noncommutative spaces, to the extent that points in phase space are now replaced by NxN matrices.
 Authors:
 Department of Mathematics and Statistics, Concordia University, 1455 Boulevard de Maisonneuve West, Montreal, Quebec, H3G 1M8 (Canada)
 (Czech Republic) and Mathematics Institute, Zitna 25, 11567 Prague 1 (Czech Republic)
 Publication Date:
 OSTI Identifier:
 20929717
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Journal of Mathematical Physics; Journal Volume: 48; Journal Issue: 5; Other Information: DOI: 10.1063/1.2721290; (c) 2007 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALGEBRA; COMMUTATION RELATIONS; DEGREES OF FREEDOM; HILBERT SPACE; MATRICES; PHASE SPACE; QUANTIZATION; QUANTUM MECHANICS
Citation Formats
Ali, S. Twareque, Englis, M., and Mathematics Institute, Silesian University at Opava, Na Rybnicku 1, 74601 Opava. Matrixvalued BerezinToeplitz quantization. United States: N. p., 2007.
Web. doi:10.1063/1.2721290.
Ali, S. Twareque, Englis, M., & Mathematics Institute, Silesian University at Opava, Na Rybnicku 1, 74601 Opava. Matrixvalued BerezinToeplitz quantization. United States. doi:10.1063/1.2721290.
Ali, S. Twareque, Englis, M., and Mathematics Institute, Silesian University at Opava, Na Rybnicku 1, 74601 Opava. Tue .
"Matrixvalued BerezinToeplitz quantization". United States.
doi:10.1063/1.2721290.
@article{osti_20929717,
title = {Matrixvalued BerezinToeplitz quantization},
author = {Ali, S. Twareque and Englis, M. and Mathematics Institute, Silesian University at Opava, Na Rybnicku 1, 74601 Opava},
abstractNote = {We generalize some earlier results on a BerezinToeplitz type of quantization on Hilbert spaces built over certain matrix domains. In the present, wider setting, the theory could be applied to systems possessing several kinematic and internal degrees of freedom. Our analysis leads to an identification of those observables, in this general context, which admit a semiclassical limit and those for which no such limit exists. It turns out that the latter class of observables involves the internal degrees of freedom in an intrinsic way. Mathematically, the theory, being a generalization of the standard BerezinToeplitz quantization, points the way to applying such a quantization technique to possibly noncommutative spaces, to the extent that points in phase space are now replaced by NxN matrices.},
doi = {10.1063/1.2721290},
journal = {Journal of Mathematical Physics},
number = 5,
volume = 48,
place = {United States},
year = {Tue May 15 00:00:00 EDT 2007},
month = {Tue May 15 00:00:00 EDT 2007}
}

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