Journal article 415 views 33 downloads
Quantum geodesic flows and curvature
,
Shahn Majid
Letters in Mathematical Physics, Volume: 113, Issue: 3
Swansea University Author:
Edwin Beggs
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DOI (Published version): 10.1007/s11005-023-01687-7
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 arise...
| Published in: | Letters in Mathematical Physics |
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| ISSN: | 0377-9017 1573-0530 |
| Published: |
Springer Science and Business Media LLC
2023
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| Online Access: |
Check full text
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| URI: | https://cronfa.swan.ac.uk/Record/cronfa65334 |
| 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 matrices, fuzzy spheres and the q-sphere. |
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| Keywords: |
Noncommutative geometry, Quantum gravity, Ricci tensor, Quantum mechanics, Fuzzy sphere, Quantum group, Quantum sphere |
| College: |
Faculty of Science and Engineering |
| Funders: |
Queen Mary, open access fee only |
| Issue: |
3 |