A Curvature Operator for a Regular Tetrahedron Shape in LQG
General Relativity and Quantum Cosmology
2019-07-03 v6
Abstract
An alternative approach introducing a 3 dimensional Ricci scalar curvature quantum operator given in terms of volume and area as well as new edge length operators is proposed. An example of monochromatic 4-valent node intertwiner state (equilateral tetrahedra) is studied and the scalar curvature measure for a regular tetrahedron shape is constructed. It is shown that all regular tetrahedron states are in the negative scalar curvature regime and for the semi-classical limit the spectrum is very close to the Euclidean regime.
Keywords
Cite
@article{arxiv.1803.03134,
title = {A Curvature Operator for a Regular Tetrahedron Shape in LQG},
author = {Omar Nemoul and Noureddine Mebarki},
journal= {arXiv preprint arXiv:1803.03134},
year = {2019}
}
Comments
16 pages, 8 figures, 1 table