Non Standard Extended Noncommutativity of Coordinates

2001/04/30 by A. Boulahoual, M. B. Sedra
Physics and Astronomy · Mathematics · #hep-th #math-ph #math.MP

paper · pdf

published as Chin.J.Phys. 42 (2004) 591-597 · 9 pages, Latex

arxiv created 2003/07/28 · arxiv updated 2009/11/30

Abstract

We present in this short note an idea about a possible extension of the standard noncommutative algebra to the formal differential operators framework. In this sense, we develop an analysis and derive an extended noncommutative structure given by [x_a, x_b]_⋆ = i(θ+ χ)_ab where θ_ab is the standard noncommutative parameter and χ_ab(x)≡ χ^μ_ab(x)∂_μ =1/2(x_a θ^μ_b - x_b θ^μ_a)∂_μ is an antisymmetric non-constant vector-field shown to play the role of the extended deformation parameter. This idea was motivated by the importance of noncommutative geometry framework, with nonconstant deformation parameter, in the current subject of string theory and D-brane physics.

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