Physics Seminar


Wednesday, Oct. 13, 2004, 4:30 pm
Willet Science Center 101

 Jose L. Balduz Jr.
Department of Physics
Mercer University



Modeling Space with Simple Graphs

Attempts are currently underway to describe the emergence of continuous space or spacetime from an underlying discrete micro-structure. For example, one may model space as arising from a graph: a countable set of nodes or locations, together with weighted links between pairs of nodes. In the simplest case the links are not weighted, they either do or do not exist. For a given simple graph, we may assign a distance to each pair of nodes, then embed the nodes in a continuous flat or curved space so that those distances are recovered. We first consider all graphs with up to four nodes, and two distinct ways to define the distances, based on simple counting and the graph Laplacian propagator. In some cases a given graph can be embedded in space of a particular dimensionality, while in some cases this is impossible. We then consider larger graphs (complete graphs, star graphs, loops and strings, random graphs) and cluster graphs, where cliques of tightly linked nodes become meta-nodes in a weighted graph (nonlocal web). This leads us to consider hypergraphs, which may be used to model spacetime causal sets and quantum fields.

Please join us for light refreshments at 4:15pm outside WSC 109.