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Quantum geodesic flows and curvature

Edwin Beggs Orcid Logo, Shahn Majid Orcid Logo

Letters in Mathematical Physics, Volume: 113, Issue: 3

Swansea University Author: Edwin Beggs Orcid Logo

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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...

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Published in: Letters in Mathematical Physics
ISSN: 0377-9017 1573-0530
Published: Springer Science and Business Media LLC 2023
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URI: https://cronfa.swan.ac.uk/Record/cronfa65334
first_indexed 2023-12-17T15:46:06Z
last_indexed 2024-11-25T14:15:52Z
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spelling 2024-03-25T12:25:08.1549375 v2 65334 2023-12-17 Quantum geodesic flows and curvature a0062e7cf6d68f05151560cdf9d14e75 0000-0002-3139-0983 Edwin Beggs Edwin Beggs true false 2023-12-17 MACS 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. Journal Article Letters in Mathematical Physics 113 3 Springer Science and Business Media LLC 0377-9017 1573-0530 Noncommutative geometry, Quantum gravity, Ricci tensor, Quantum mechanics, Fuzzy sphere, Quantum group, Quantum sphere 22 6 2023 2023-06-22 10.1007/s11005-023-01687-7 http://dx.doi.org/10.1007/s11005-023-01687-7 COLLEGE NANME Mathematics and Computer Science School COLLEGE CODE MACS Swansea University Another institution paid the OA fee Queen Mary, open access fee only 2024-03-25T12:25:08.1549375 2023-12-17T15:36:58.4341013 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics Edwin Beggs 0000-0002-3139-0983 1 Shahn Majid 0000-0003-1657-5434 2 65334__29824__7ba905b8b2d646c6a9e59cc8494acab7.pdf 65334.VOR.pdf 2024-03-25T12:22:18.4516434 Output 984751 application/pdf Version of Record true 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. true eng http://creativecommons.org/licenses/by/4.0/
title Quantum geodesic flows and curvature
spellingShingle Quantum geodesic flows and curvature
Edwin Beggs
title_short Quantum geodesic flows and curvature
title_full Quantum geodesic flows and curvature
title_fullStr Quantum geodesic flows and curvature
title_full_unstemmed Quantum geodesic flows and curvature
title_sort Quantum geodesic flows and curvature
author_id_str_mv a0062e7cf6d68f05151560cdf9d14e75
author_id_fullname_str_mv a0062e7cf6d68f05151560cdf9d14e75_***_Edwin Beggs
author Edwin Beggs
author2 Edwin Beggs
Shahn Majid
format Journal article
container_title Letters in Mathematical Physics
container_volume 113
container_issue 3
publishDate 2023
institution Swansea University
issn 0377-9017
1573-0530
doi_str_mv 10.1007/s11005-023-01687-7
publisher Springer Science and Business Media LLC
college_str Faculty of Science and Engineering
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hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Mathematics and Computer Science - Mathematics{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Mathematics and Computer Science - Mathematics
url http://dx.doi.org/10.1007/s11005-023-01687-7
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description 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.
published_date 2023-06-22T08:10:29Z
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score 11.056209

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