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

Physics

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https://doi.org/10.1063/1.532003
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Keywords

MANIFOLDS, CONNECTIONS, QUANTIZATION

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A natural basis of states for the noncommutative sphere and its Moyal bracket. / Gratus, J.
In: Journal of Mathematical Physics, Vol. 38, No. 8, 08.1997, p. 4283-4300.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Bibtex

@article{21736bb469dc433a8b63900bfa9a10ef,

title = "A natural basis of states for the noncommutative sphere and its Moyal bracket",

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.",

keywords = "MANIFOLDS, CONNECTIONS, QUANTIZATION",

author = "J Gratus",

year = "1997",

month = aug,

doi = "10.1063/1.532003",

language = "English",

volume = "38",

pages = "4283--4300",

journal = "Journal of Mathematical Physics",

issn = "0022-2488",

publisher = "American Institute of Physics Publising LLC",

number = "8",

}

RIS

TY - JOUR

T1 - A natural basis of states for the noncommutative sphere and its Moyal bracket

AU - Gratus, J

PY - 1997/8

Y1 - 1997/8

N2 - 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.

AB - 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.

KW - MANIFOLDS

KW - CONNECTIONS

KW - QUANTIZATION

U2 - 10.1063/1.532003

DO - 10.1063/1.532003

M3 - Journal article

VL - 38

SP - 4283

EP - 4300

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

SN - 0022-2488

IS - 8

ER -

Research

Text available via DOI:

Keywords