München 1997 – wissenschaftliches Programm

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MP: Theoretische und Mathematische Grundlagen der Physik

MP 10: Gravitation und Quantentheorie

MP 10.8: Fachvortrag

Donnerstag, 20. März 1997, 16:40–17:00, HS 118

Planck-Scale Physics within the Framework of ’Non-Commutative Geometry’ and ’Random Graphs’ — •Manfred Requardt — Institut fuer Theoretische Physik, Universitaet Goettingen, Bunsenstr. 9, 37073 Goettingen

Starting from the hypothesis that both physics and the corres- ponding mathematics are discrete on the Planck scale, we develop a certain framework in form of a class of ’dynamical cellular networks’ which incorporates as ingredients pieces from ’non- commutative geometry’ and, on the other side, the theory of ’random graphs’. With the help of these concepts we develop, among other things, a version of discrete analysis and topology/ geometry on networks and graphs and the like. Our main emphasis lies on the description of the phase transition like emergence of a ’super structure’ within the network/graph consisting of an array of densely entangled subclusters of constituents, which are then identified with the physical protopoints of our space-time manifold or physical vacuum. It is one of our goals or rather: hopes to exhibit how the non-commutative geometry of e.g. Connes and Lott may arise via some sort of coarse graining from our Planck scale approach. References: hep-th/9605103, hep-th/ 9610055.