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Quantum geodesic flows on graphs
,
Shahn Majid
Letters in Mathematical Physics, Volume: 114, Issue: 5
Swansea University Author:
Edwin Beggs
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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...
| Published in: | Letters in Mathematical Physics |
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| ISSN: | 1573-0530 |
| Published: |
Springer Science and Business Media LLC
2024
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| Online Access: |
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| URI: | https://cronfa.swan.ac.uk/Record/cronfa67840 |
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| 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 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. |
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| Keywords: |
noncommutative geometry, graph, calculus |
| College: |
Faculty of Science and Engineering |
| Funders: |
No funds, grants or other support was received. |
| Issue: |
5 |