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Quantum geodesic flows and curvature.
- Source :
-
Letters in Mathematical Physics . Jun2023, Vol. 113 Issue 3, p1-44. 44p. - Publication Year :
- 2023
-
Abstract
- We study geodesics flows on curved quantum Riemannian geometries using a recent formulation in terms of bimodule connections and completely positive maps. We complete this formalism with a canonical ∗ operation on noncommutative vector fields. We show on a classical manifold how the Ricci tensor arises naturally in our approach as a term in the convective derivative of the divergence of the geodesic velocity field and use this to propose a similar object in the noncommutative case. Examples include quantum geodesic flows on the algebra of 2 × 2 matrices, fuzzy spheres and the q-sphere. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 03779017
- Volume :
- 113
- Issue :
- 3
- Database :
- Academic Search Index
- Journal :
- Letters in Mathematical Physics
- Publication Type :
- Academic Journal
- Accession number :
- 164482526
- Full Text :
- https://doi.org/10.1007/s11005-023-01687-7