Noncommutative theories and general coordinate transformations

2004/09/30 by C. D. Fosco, Gonzalo Torroba, G. Torroba
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Algebra over a field #Black Holes and Theoretical Physics #Mathematics #Noncommutative and Quantum Gravity Theories #Noncommutative geometry #Pure mathematics #hep-th

paper · pdf · doi:10.1103/physrevd.71.065012

published as Phys.Rev. D71 (2005) 065012 · 21 pages, no figures, LaTeX. v2: section 5 added, typos corrected. Version to appear in Physical Review D

arxiv created 2005/03/18 · openalex publication_date 2005/03/24 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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\ensuremathθ_ij, with a constant \ensuremathθ_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 \ensuremathθ_ij is constant.

Citations

• Action functional for kappa-Minkowski Noncommutative Spacetime
• Effective field theories on noncommutative space-time
• Construction of gauge theories on curved noncommutative spacetime
• Deformation Quantization of Poisson Manifolds
• Gauge theory on noncommutative spaces