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Journal of Physical Studies 20(1/2), Article 1001 [5 pages] (2016)
DOI: https://doi.org/10.30970/jps.20.1001 MINIMAL LENGTH, AREA, AND VOLUME IN A SPACE WITH NONCOMMUTATIVITY OF COORDINATESKh. P. Gnatenko, V. M. Tkachuk
Department for Theoretical Physics, Ivan Franko National University of Lviv, |
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We study a space in which spatial coordinates do not commute. We consider a noncommutative space of the canonical type characterised by the constant antisymmetric matrix of noncommutativity. Length, area, and volume are limited below in this space. The corresponding minimal values are determined by the elements of the matrix of noncommutativity. We examine the minimal length, area, and volume in a noncommutative space of the canonical type with the preserved rotational symmetry which has been proposed in our previous paper [Kh. P. Gnatenko, V. M. Tkachuk, Phys. Lett. A \textbf{378}, 3509 (2014)]. The corresponding rotationally invariant noncommutative algebra is constructed with the help of the generalization of the parameter of noncommutativity to a tensor. The latter is constructed with the help of additional coordinates that are governed by a rotationally symmetric system. It is shown that in the rotationally invariant noncommutative space there is a minimal length which is determined by the mean value of the tensor of noncommutativity. On the contrast to the canonical version of noncommutativity in the rotationally invariant noncommutative space the area and volume are not constrained.
PACS number(s): 02.40.Gh, 03.65.-w