English

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