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Quantum geodesic flows on graphs

Edwin Beggs Orcid Logo, Shahn Majid, QMUL

Letters in Mathematical Physics, Volume: Volume 114,, Issue: article number 112, (2024)

Swansea University Author: Edwin Beggs Orcid Logo

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DOI (Published version): https://link.springer.com/article/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: https://link.springer.com/journal/11005
Published: Springer 2024
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URI: https://cronfa.swan.ac.uk/Record/cronfa67840
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first_indexed 2024-09-26T09:50:37Z
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 Volume 114, article number 112, (2024) Springer https://link.springer.com/journal/11005 noncommutative geometry, graph, calculus 16 9 2024 2024-09-16 https://link.springer.com/article/10.1007/s11005-024-01860-6 https://link.springer.com/article/10.1007/s11005-024-01860-6 COLLEGE NANME Mathematics and Computer Science School COLLEGE CODE MACS Swansea University Another institution paid the OA fee 2024-09-26T10:50:38.1095827 2024-09-26T10:40:51.0144899 College of Science Edwin Beggs 0000-0002-3139-0983 1 Shahn Majid, QMUL 2
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, QMUL
format Journal article
container_title Letters in Mathematical Physics
container_volume Volume 114,
container_issue article number 112, (2024)
publishDate 2024
institution Swansea University
issn https://link.springer.com/journal/11005
doi_str_mv https://link.springer.com/article/10.1007/s11005-024-01860-6
publisher Springer
college_str College of Science
hierarchytype
hierarchy_top_id collegeofscience
hierarchy_top_title College of Science
hierarchy_parent_id collegeofscience
hierarchy_parent_title College of Science
url https://link.springer.com/article/10.1007/s11005-024-01860-6
document_store_str 0
active_str 0
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 2024-09-16T10:50:37Z
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score 11.029921

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