Remarks about Metric Tensors on Fractal Structures
In 1978 Hawking  presented considerations concerning the nature of spacetime on the very short length scale (i.e. of Planck length). He was motivated by Wheeler’s  suggestion concerning the existence of a very large fluctuation of the metric of the space-time manifold on short length scales. The reason for this was that for example unlike to the Yang-Mills case the action for the gravitational field: is not scale invariant. While using the path integral approach considered as the best method of quantizing gauge fields  one realizes immediately that a large fluctuation of a metric over a short length scale is not highly damped in the path integral. In supergravity theories as well one cannot use the usual Feynman diagram expansion around flat space due to the lack of a scale invariance of space-time volume.
KeywordsSupergravity Theory Planck Length Sierpinski Gasket Path Integral Approach Short Length Scale
Unable to display preview. Download preview PDF.
- 2.J.A.Wheeler, in Relativity groups and topology, ed. B.S. and C.M.DeWitt (Gordan and Breach, New York 1964)Google Scholar
- 4.F.Englert, CERN-TH.4091/85Google Scholar
- 8.K.Svozil, see contribution in this volumeGoogle Scholar
- 10.K.Svozil, Technical Univ. Vienna preprint Sept. 1985Google Scholar
- 11.C. Jarlskog and F.J. Yndurain, CERN-TH.4244/85, August 1985Google Scholar
- 12.B. Müller and A. Schäfer, University of Frankfurt preprint, June 1985Google Scholar
- 13.K. Kuratowski, Topology I and II, Academic Press 1966Google Scholar
- 15.Ph.Combe, Private CommunicationGoogle Scholar