Statistical discrete geometry
Abstract
Following our earlier work, we construct statistical discrete geometry by applying statistical mechanics to discrete (Regge) gravity. We propose a coarse-graining method for discrete geometry under the assumptions of atomism and background independence. To maintain these assumptions, restrictions are given to the theory by introducing cut-offs, both in ultraviolet and infrared regime. Having a well-defined statistical picture of discrete Regge geometry, we take the infinite degrees of freedom (large n) limit. We argue that the correct limit consistent with the restrictions and the background independence concept is not the continuum limit of statistical mechanics, but the thermodynamical limit.
Cite
@article{arxiv.1607.08629,
title = {Statistical discrete geometry},
author = {Seramika Ariwahjoedi and Valerio Astuti and Jusak Sali Kosasih and Carlo Rovelli and Freddy Permana Zen},
journal= {arXiv preprint arXiv:1607.08629},
year = {2016}
}
Comments
18 pages, 16 figures, the information contained in this article was extracted from a doctoral thesis by the author