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Quantum geodesic flows on graphs

Edwin Beggs Orcid Logo, Shahn Majid Orcid Logo

Letters in Mathematical Physics, Volume: 114, Issue: 5

Swansea University Author: Edwin Beggs Orcid Logo

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DOI (Published version): 10.1007/s11005-024-01860-6

Abstract

We revisit the construction of quantum Riemannian geometries on graphs starting from a hermitian metric compatible connection, which always exists. We use this method to find quantum Levi-Civita connections on the n-leg star graph for and find the same phenomenon as recently found for the Dynkin gra...

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Published in: Letters in Mathematical Physics
ISSN: 1573-0530
Published: Springer Science and Business Media LLC 2024
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URI: https://cronfa.swan.ac.uk/Record/cronfa67840
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last_indexed 2024-09-26T09:50:37Z
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spelling v2 67840 2024-09-26 Quantum geodesic flows on graphs a0062e7cf6d68f05151560cdf9d14e75 0000-0002-3139-0983 Edwin Beggs Edwin Beggs true false 2024-09-26 MACS We revisit the construction of quantum Riemannian geometries on graphs starting from a hermitian metric compatible connection, which always exists. We use this method to find quantum Levi-Civita connections on the n-leg star graph for and find the same phenomenon as recently found for the Dynkin graph that the metric length for each inbound arrow has to exceed the length in the other direction by a multiple, here . We then study quantum geodesics on graphs and construct these on the 4-leg graph and on the integer lattice line with a general edge-symmetric metric. Journal Article Letters in Mathematical Physics 114 5 Springer Science and Business Media LLC 1573-0530 noncommutative geometry, graph, calculus 16 9 2024 2024-09-16 10.1007/s11005-024-01860-6 COLLEGE NANME Mathematics and Computer Science School COLLEGE CODE MACS Swansea University Another institution paid the OA fee No funds, grants or other support was received. 2024-10-16T12:32:07.7787120 2024-09-26T10:40:51.0144899 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 67840__31458__2d393caa79fb46a688cfed4140ac915b.pdf s11005-024-01860-6.pdf 2024-09-26T10:49:07.4768937 Output 1110830 application/pdf Version of Record true © The Author(s) 2024. This article is licensed under a Creative Commons Attribution 4.0 International License. true eng http://creativecommons.org/licenses/by/4.0/
title Quantum geodesic flows on graphs
spellingShingle Quantum geodesic flows on graphs
Edwin Beggs
title_short Quantum geodesic flows on graphs
title_full Quantum geodesic flows on graphs
title_fullStr Quantum geodesic flows on graphs
title_full_unstemmed Quantum geodesic flows on graphs
title_sort Quantum geodesic flows on graphs
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 114
container_issue 5
publishDate 2024
institution Swansea University
issn 1573-0530
doi_str_mv 10.1007/s11005-024-01860-6
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
document_store_str 1
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description We revisit the construction of quantum Riemannian geometries on graphs starting from a hermitian metric compatible connection, which always exists. We use this method to find quantum Levi-Civita connections on the n-leg star graph for and find the same phenomenon as recently found for the Dynkin graph that the metric length for each inbound arrow has to exceed the length in the other direction by a multiple, here . We then study quantum geodesics on graphs and construct these on the 4-leg graph and on the integer lattice line with a general edge-symmetric metric.
published_date 2024-09-16T12:32:05Z
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score 11.035634

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