Year: 2013
Type: preprint
Abstract: The connection between angular momentum in quantum mechanics and geometric objects is extended to manifold with torsion. First, we notice the relation between the $6j$ symbol and Regge's discrete version of the action functional of Euclidean three dimensional gravity with torsion, then consider the Ponzano and Regge asymptotic formula for the Wigner $6j$ symbol on this simplicial manifold with torsion. In this approach, a three dimensional manifold $M$ is decomposed into a collection of tetrahedra, and it is assumed that each tetrahedron is filled in with flat space and the torsion of $M$ is concentrated on the edges of the tetrahedron, the length of the edge is chosen to be proportional to the length of the angular momentum vector in semiclassical limit. The Einstein-Hilbert action is then a function of the angular momentum and the Burgers vector of dislocation, and it is given by summing the Regge action over all tetrahedra in $M$. We also discuss the asymptotic approximation of the partition function and their relation to the Feynmann path integral for simplicial manifold with torsion without cosmological constant.
Source: arXiv (Cornell University)
Author: Vargas, T
Institution: National University of San Marcos
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1847050312