Analytical description of scale-dependent topology. A toy model

Details Analytical description of scale-dependent topology. A toy model Analytical description of scale-dependent topology. A toy model

Dec 1993

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1993phlb..319...74s&link_type=abstract

Physics Letters B, Volume 319, Issue 1-3, p. 74-82.

Physics

8

Scientific paper

Based on a (2+1)-dimensional toy model, we present one analytical description of the scale-dependent effective topology of the space-time foam. We describe it in terms of a scattering cross-section. We begin by preparing a two-dimensional space with one topological handle, regarding it as the most elementary building block for the foam-like structure. We then calculate the scattering cross-section of a scalar field on this space. We investigate, how the scattering cross-section changes depending on the variety of topologies as well as the incident energy scale. We also investigate how a twist of the handle affects the cross-section. We find out a systematic topology-dependence and a twist effect in the cross-section. We also try to sketch briefly some basic points of the topological approximation procedure in terms of the homology group.
Present address: Inter-University Centre for Astronomy and Astrophysics, Post Bag 4, Pune 411007, India

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