Noncommutative theories and general coordinate transformations

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 $[y_i,y_j]=i{\theta }_{ij}$, 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.

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

References in corpus (3)

• Perfect Fluid Theory and its Extensions
• Action functional for kappa-Minkowski Noncommutative Spacetime
• On Coordinate Transformations in Planar Noncommutative Theories

Cited by in corpus (4)

• Exotic galilean symmetry and non-commutative mechanics
• Position-dependent noncommutative products: classical construction and field theory
• Non-constant Non-commutativity in 2d Field Theories and a New Look at Fuzzy Monopoles
• A Perturbative Approach to Fuzzifying Field Theories