Noncommutative geometry and gravity
By P. Aschieri, M. Dimitrijević, F. Meyer, J. Wess. 2005
416 citations recorded by the source corpus.
We study a deformation of infinitesimal diffeomorphisms of a smooth manifold. The deformation is based on a general twist. This leads to a differential geometry on a noncommutative algebra of functions whose product is a star product. The class of noncommutative spaces studied is very rich. Non-anticommutative superspaces are also briefly considered. The differential geometry developed is covariant under deformed diffeomorphisms and is coordinate independent. The main target of this work is the construction of Einstein's equations for gravity on noncommutative manifolds.
Subfields: Mathematical Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/680c3377b03d19672208d7d6215ae9a1d25b0b72
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Citations in the corpus
- Emergent gravity from noncommutative gauge theory (2007, background): “e transformations and diffeomorphisms certainly deserves further investigations, see also [32,52] for related discussion. It remains to be seen whether the generalized notions of symmetry developed in [17] are applicable in the context of matrix models. 5 Remarks on the quantization The great virtue ”
- Symmetry, gravity and noncommutativity (2006, methodology): “ith the star-product in Aθ. One can now repeat the construction of Section 4.3 to get a noncommutative theory of gravity which is covariant under deformed diffeomorphisms and is coordinate-independent [9]. The three types of noncommutative spaces appearing in the expansion (5.24) all fall into this c”
- Yang-Baxter deformations, AdS/CFT, and twist-noncommutative gauge theory (2015, neutral): “[36–38] and the reviews [39,40].”