Noncommutative theories and general coordinate transformations

CESAR FOSCO; GONZALO TORROBA

PHYSICAL REVIEW D

AMER PHYSICAL SOC

Lugar: New York; Año: 2005 vol. 71 p. 1 - 9

1550-7998

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.