Schliemann, John (2013) The large-volume limit of a quantum tetrahedron is a quantum harmonic oscillator. CLASSICAL AND QUANTUM GRAVITY, 30 (23): 235018. ISSN 0264-9381, 1361-6382
Full text not available from this repository. (Request a copy)Abstract
It is shown that the volume operator of a quantum tetrahedron is, in the sector of large eigenvalues, accurately described by a quantum harmonic oscillator. This result relies on the fact that (i) the volume operator couples only neighboring states of its standard basis, and (ii) its matrix elements show a unique maximum as a function of internal angular momentum quantum numbers. These quantum numbers, considered as a continuous variable, are the coordinate of the oscillator describing its quadratic potential, while the corresponding derivative defines a momentum operator. We also analyze the scaling properties of the oscillator parameters as a function of the size of the tetrahedron, and the role of different angular momentum coupling schemes.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | TRIAD OPERATOR QUANTIZATION; CONSISTENCY CHECK; SPIN NETWORKS; GRAVITY; EIGENVALUES; GEOMETRY; |
| Subjects: | 500 Science > 530 Physics |
| Divisions: | Physics > Institute of Theroretical Physics Physics > Institute of Theroretical Physics > Chair Professor Grifoni > Group John Schliemann |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 23 Mar 2020 10:06 |
| Last Modified: | 23 Mar 2020 10:06 |
| URI: | https://pred.uni-regensburg.de/id/eprint/15534 |
Actions (login required)
 |
View Item |
