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A natural basis of states for the noncommutative sphere and its Moyal bracket

Gratus, J (1997) A natural basis of states for the noncommutative sphere and its Moyal bracket. Journal of Mathematical Physics, 38 (8). pp. 4283-4300. ISSN 0022-2488

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Abstract

An infinite-dimensional algebra which is a nondecomposable reducible representation of su(2) is given. This algebra is defined with respect to two real parameters. If one of these parameters is zero, the algebra is the commutative algebra of functions on the sphere, otherwise it is a noncommutative analog. This is an extension of the algebra normally referred to as the (Berezin) quantum sphere or ''fuzzy'' sphere. A natural indefinite ''inner'' product and a basis of the algebra orthogonal with respect to it are given. The basis elements are homogeneous polynomials, eigenvectors of a Laplacian, and related to the Hahn polynomials. It is shown that these elements tend to the spherical harmonics far the sphere. A Moyal bracket is constructed and shown to be the standard Moyal bracket for the sphere. (C) 1997 American Institute of Physics.

Item Type: Article
Journal or Publication Title: Journal of Mathematical Physics
Uncontrolled Keywords: MANIFOLDS ; CONNECTIONS ; QUANTIZATION
Subjects:
Departments: Faculty of Science and Technology > Physics
ID Code: 64125
Deposited By: ep_importer_pure
Deposited On: 14 May 2013 16:12
Refereed?: Yes
Published?: Published
Last Modified: 22 Nov 2017 22:52
Identification Number:
URI: http://eprints.lancs.ac.uk/id/eprint/64125

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