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Coherent states on Hilbert modules

Ali, Twareque S and Bhattacharyya, T and Roy, SS (2011) Coherent states on Hilbert modules. In: Journal of Physics A: Mathematical and Theoretical, 44 (27).

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Official URL: http://iopscience.iop.org/1751-8121/44/27/275202/


We generalize the concept of coherent states, traditionally defined as special families of vectors on Hilbert spaces, to Hilbert modules. We show that Hilbert modules over C*-algebras are the natural settings for a generalization of coherent states defined on Hilbert spaces. We consider those Hilbert C*-modules which have a natural left action from another C*-algebra, say A. The coherent states are well defined in this case and they behave well with respect to the left action by A. Certain classical objects like the Cuntz algebra are related to specific examples of coherent states. Finally we show that coherent states on modules give rise to a completely positive definite kernel between two C*-algebras, in complete analogy to the Hilbert space situation. Related to this, there is a dilation result for positive operator-valued measures, in the sense of Naimark. A number of examples are worked out to illustrate the theory. Some possible physical applications are also mentioned.

Item Type: Journal Article
Publication: Journal of Physics A: Mathematical and Theoretical
Publisher: IOP Publishing ltd
Additional Information: Copyright of this article belongs to IOP Publishing ltd.
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Date Deposited: 29 Jun 2011 09:05
Last Modified: 29 Jun 2011 09:05
URI: http://eprints.iisc.ac.in/id/eprint/38629

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