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Noncommutative theories and general coordinate transformations

C. D. Fosco·G. Torroba
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Abstract

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 $[y_i, y_j] = i θ_{ij}$, with a constant $θ_{ij}$ 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 $θ_{ij}$ is constant.

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C. D. Fosco, G. Torroba. 2005-03-18. Noncommutative theories and general coordinate transformations. https://doi.org/10.1103/physrevd.71.065012

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