Quantum states of elementary three-geometry

Details Quantum states of elementary three-geometry Quantum states of elementary three-geometry

2001-12-18

arxiv.org/abs/gr-qc/0112043v1

Class.Quant.Grav. 19 (2002) 3761-3774

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

15 pages, LaTex

Scientific paper

10.1088/0264-9381/19/14/315

We introduce a quantum volume operator $K$ in three--dimensional Quantum Gravity by taking into account a symmetrical coupling scheme of three SU(2) angular momenta. The spectrum of $K$ is discrete and defines a complete set of eigenvectors which is alternative with respect to the complete sets employed when the usual binary coupling schemes of angular momenta are considered. Each of these states, that we call quantum bubbles, represents an interference of extended configurations which provides a rigorous meaning to the heuristic notion of quantum tetrahedron. We study the generalized recoupling coefficients connecting the symmetrical and the binary basis vectors, and provide an explicit recursive solution for such coefficients by analyzing also its asymptotic limit.

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