Graph-Laplacians and Dirac Operators on (Infinite) Graphs and the Calculation of the Connes-Distance-Functional
| dc.creator | Requardt, Manfred | |
| dc.date | 2000-01-18 | |
| dc.date | 2000-08-23 | |
| dc.date.accessioned | 2026-07-07T04:27:36Z | |
| dc.date.available | 2026-07-07T04:27:36Z | |
| dc.description | We develop a graph-Hilbert-space framework, inspired by non-commutative geometry, on (infinite) graphs and use it to study spectral properies of \tit{graph-Laplacians} and so-called \tit{graph-Dirac-operators}. Putting the various pieces together we define a {\it spectral triplet} sharing most (if not all, depending on the particular graph model) of the properties of what Connes calls a \tit{spectral triple}. With the help of this scheme we derive an explicit expression for the {\it Connes-distance function} on general graphs and prove both a variety of apriori estimates for it and calculate it for certain examples of graphs. As a possibly interesting aside, we show that the natural setting of approaching such problems may be the framework of \tit{(non-)linear programming} or \tit{optimization}. We compare our results (arrived at within our particular framework) with the results of other authors and show that the seeming differences depend on the use of different graph-geometries and/or Dirac operators. | |
| dc.description | 27 pages, Latex, some more references and comments referring to existing work, some proofs improved and several new results included, the relation of distance calculations to non-linear optimization clarified, under consideration by JPA | |
| dc.identifier | https://arxiv.org/abs/math-ph/0001026 | |
| dc.identifier | http://arxiv.org/abs/math-ph/0001026 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/56474 | |
| dc.subject | Mathematical Physics | |
| dc.subject | High Energy Physics - Theory | |
| dc.title | Graph-Laplacians and Dirac Operators on (Infinite) Graphs and the Calculation of the Connes-Distance-Functional | |
| dc.type | text |