T. Nowotny et M. Requardt, Pregeometric concepts on graphs and cellular networks as possible models of space-time at the Planck-scale, CHAOS SOL F, 10(2-3), 1999, pp. 469-481
Starting from the working hypothesis that both physics and the correspondin
g mathematics have to be described by means of discrete concepts on the Pla
nck-scale, one of the many problems one has to face is to find the discrete
protoforms of the building blocks of continuum physics and mathematics. In
the following we embark on developing such concepts for irregular structur
es like (large) graphs or networks which are intended to emulate (some of)
the generic properties of the presumed combinatorial substratum from which
continuum physics is assumed to emerge as a coarse grained and secondary mo
del theory We briefly indicate how various concepts of discrete (functional
) analysis and geometry can be naturally constructed within this Framework,
leaving a larger portion of the paper to the systematic developement of di
mensional concepts and their properties, which may have a possible bearing
on various branches of modern physics beyond quantum gravity. (C) 1999 Else
vier Science Ltd. All rights reserved.