Noncommutative theories and general coordinate transformations

Details Noncommutative theories and general coordinate transformations Noncommutative theories and general coordinate transformations

2004-09-23

arxiv.org/abs/hep-th/0409240v2

Phys.Rev. D71 (2005) 065012

Physics

High Energy Physics

High Energy Physics - Theory

21 pages, no figures, LaTeX. v2: section 5 added, typos corrected. Version to appear in Physical Review D

Scientific paper

10.1103/PhysRevD.71.065012

We study the class of noncommutative theories in $d$ dimensions whose spatial coordinates $(x_i)_{i=1}^d$ can be obtained by performing a smooth change of variables on $(y_i)_{i=1}^d$, the coordinates of a standard noncommutative theory, which satisfy the relation $[y_i, y_j] = i \theta_{ij}$, with a constant $\theta_{ij}$ tensor. The $x_i$ variables verify a commutation relation which is, in general, space-dependent. We study the main properties of this special kind of noncommutative theory and show explicitly that, in two dimensions, any theory with a space-dependent commutation relation can be mapped to another where that $\theta_{ij}$ is constant.

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