2002/02/28 by Ali H. Chamseddine, A. H. Chamseddine · 69 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Classical mechanics #Cosmology and Gravitation Theories #Gravitation #Invariant (physics) #Mathematical physics #Mathematics #Noncommutative algebraic geometry #Noncommutative and Quantum Gravity Theories #Noncommutative geometry #Noncommutative quantum field theory #Physics #Pure mathematics #Quantum differential calculus #Unitary state #hep-th
paper · pdf · doi:10.1063/1.1572199
published in Journal of Mathematical Physics 44(6), 2534-2541 (American Institute of Physics) · 11 pages. Paper shortened. Consideration is now limited to gravity in four-dimensions
arxiv created 2002/11/21 · openalex publication_date 2003/05/21 · arxiv updated 2015/06/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Two main problems face the construction of noncommutative actions for gravity with star products: the complex metric and finding an invariant measure. The only gauge groups that could be used with star products are the unitary groups. I propose an invariant gravitational action in D=4 dimensions based on the constrained gauge group U(2,2) broken to U(1,1)×U(1,1). No metric is used, thus giving a naturally invariant measure. This action is generalized to the noncommutative case by replacing ordinary products with star products. The four-dimensional noncommutative action is studied and the deformed action to first order in deformation parameter is computed.