Journal article 130 views 4 downloads
Quantum geodesic flows and curvature
,
Shahn Majid
Letters in Mathematical Physics, Volume: 113, Issue: 3
Swansea University Author:
Edwin Beggs
-
PDF | Version of Record
This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.
Download (961.67KB)
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 |
|---|---|
| ISSN: | 0377-9017 1573-0530 |
| Published: |
Springer Science and Business Media LLC
2023
|
| Online Access: |
Check full text
|
| URI: | https://cronfa.swan.ac.uk/Record/cronfa65334 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| 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. |
|---|---|
| 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 |