First order approach and index theorems for discrete and metric graphs
| dc.creator | Post, Olaf | |
| dc.date | 2007-08-28 | |
| dc.date | 2007-09-03 | |
| dc.date.accessioned | 2026-07-07T08:26:50Z | |
| dc.date.available | 2026-07-07T08:26:50Z | |
| dc.description | The aim of the present paper is to introduce the notion of first order (supersymmetric) Dirac operators on discrete and metric (``quantum'') graphs. In order to cover all self-adjoint boundary conditions for the associated metric graph Laplacian, we develop systematically a new type of discrete graph operators acting on a decorated graph. The decoration at each vertex of degree-d is given by a subspace of $\C^d$, generalising the fact that a function on the standard vertex space has only a scalar value. We develop the notion of exterior derivative, differential forms, Dirac and Laplace operators in the discrete and metric case, using a supersymmetric framework. We calculate the (supersymmetric) index of the discrete Dirac operator generalising the standard index formula involving the Euler characteristic of a graph. Finally, we show that the corresponding index for the metric Dirac operator agrees with the discrete one. | |
| dc.description | 36 pages, some references added | |
| dc.identifier | https://arxiv.org/abs/0708.3707 | |
| dc.identifier | http://arxiv.org/abs/0708.3707 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/137074 | |
| dc.subject | Spectral Theory | |
| dc.subject | Mathematical Physics | |
| dc.subject | Combinatorics | |
| dc.subject | Functional Analysis | |
| dc.title | First order approach and index theorems for discrete and metric graphs | |
| dc.type | text |