Coherent state induced star product on R**3(lambda) and the fuzzy sphere

Hammou, A.B.; Lagraa, M.; Sheikh-Jabbari, M.M.

doi:10.1103/PhysRevD.66.025025

Coherent state induced star product on R**3(lambda) and the fuzzy sphere

A.B. Hammou
(
- ICTP, Trieste
)
,
M. Lagraa
(
- ICTP, Trieste and
- Oran U.
)
,
M.M. Sheikh-Jabbari
(
- Stanford U., Phys. Dept.
)

Oct, 2001

24 pages

Published in:

Phys.Rev.D 66 (2002) 025025

e-Print:

hep-th/0110291 [hep-th]

DOI:

10.1103/PhysRevD.66.025025

Report number:

SU-ITP-01-043,
IC-2001-58

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Abstract:

Using the Hopf fibration and starting from a four dimensional noncommutative Moyal plane,

R^2_{\theta}\times R^2_{\theta}

, we obtain a star-product for the noncommutative (fuzzy)

R^3_{\lambda}

defined by

[x^i,x^j]=i\lambda\epsilon_{ijk}x^k

. Furthermore, we show that there is a projection function which allows us to reduce the functions on

R^3_{\lambda}

to that of the fuzzy sphere, and hence we introduce a new star-product on the fuzzy sphere. We will then briefly discuss how using our method one can extract information about the field theory on fuzzy sphere and \rrlam from the corresponding field theories on

R_{theta}\times R_{\theta}

space.

11.15.-q
12.15.-y
11.25.-w
12.60.-i
differential geometry: noncommutative
sphere: fuzzy
coherent state
operator: algebra
field theory

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