https://doi.org/10.1140/epjc/s10052-012-1919-z
Regular Article - Theoretical Physics
From the generalized uncertainty relations on fuzzy AdS 2 to the Poincaré geometry
1
Department of Theoretical Physics and Astrophysics, Faculty of Physics, University of Tabriz, P. O. Box 51666-16471, Tabriz, Iran
2
School of Physics, Institute for Research in Fundamental Sciences (IPM), P. O. Box 19395-5531, Tehran, Iran
* e-mail: hfakhri@tabrizu.ac.ir
Received:
18
September
2011
Revised:
9
January
2012
Published online:
10
March
2012
The positive and discrete unitary irreps of SU(1,1) are used to construct fuzzy (Euclidean) AdS 2. Two different types of uncertainty relation involving the Weyl–Heisenberg and a weaker type are studied. It is shown that there are no generalized coherent states which simultaneously minimize the Weyl–Heisenberg uncertainty relations among three non-commuting embedding coordinates of the fuzzy AdS 2. However, generalized squeezed states that simultaneously satisfy the three weaker uncertainty relations do exist, and reproduce some properties of the classical AdS 2. Up to a common scaling factor in terms of the irrep label, the expectation values of the non-commuting coordinates over such states are described in the same manner as the classical AdS 2, in terms of the Poincaré coordinates. The expectation values on the fuzzy AdS 2 tend to their corresponding values in the commutative limit.
© Springer-Verlag / Società Italiana di Fisica, 2012
