Regensburg 1998 – wissenschaftliches Programm

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MP: Theoretische und Mathematische Grundlagen der Physik

MP 7: Strukturelle Fragen der Quantenfeldtheorie

MP 7.7: Fachvortrag

Donnerstag, 26. März 1998, 16:40–17:00, H45

Dimension Theory of Graphs and Networks — •Thomas Nowotny and Manfred Requardt — Institut für Theoretische Physik, Universität Göttingen, Bunsenstraße 9, 37073 Göttingen

Quite a few physicists nowadays are convinced that space-time close to or at the Planck-scale has to be described with concepts of discrete mathematics. To be able to do so it is necessary to develop adequate conceptual and mathematical tools. One of the core concepts in both physics and mathematics is the idea of dimension. Therefore we recently proposed two definitions to introduce dimensional concepts to discrete spaces described by graphs or, in more physical terms, by networks.

The definitions are presented and the properties of these dimensional concepts are discussed. Among other things it can be shown that our definitions allow consistent results for a large number of graphs and that the dimensions thus defined are stable under a wide class of perturbations. Furthermore spaces with almost arbitrary fractal dimension can easily be constructed which may also be useful e.g. in statistical mechanics on irregular sets or for “dimensional renormalization”.
[1] T. Nowotny, M. Requardt, Göttingen preprint (submitted to J. Phys.
[1] A), hep-th/9707082