A unified vision of the symmetric coupling of angular momenta and of the quantum mechanical volume operator is illustrated. The focus is on the quantum mechanical angular momentum theory of Wignerâ€™s 6j symbols and on the volume operator of the symmetric coupling in spin network approaches: here, crucial to our presentation are an appreciation of the role of the Racah sum rule and the simplification arising from the use of Regge symmetry. The projective geometry approach permits the introduction of a symmetric representation of a network of seven spins or angular momenta. Results of extensive computational investigations are summarized, presented and briefly discussed.

Publication

In: Murgante B. et al. (eds) Computational Science and Its Applications - *ICCSA 2014*. **Lecture Notes in Computer Science**, vol 8579. Springer, Cham

Date

January, 2014

Bibtex:

```
@InCollection{Marinelli:2014jma,
Title = {{Symmetric angular momentum coupling, the quantum volume operator and the 7-spin network: a computational perspective}},
Author = {Marinelli, Dimitri and Marzuoli, Annalisa and Aquilanti, Vincenzo and Anderson, Roger W. and Bitencourt, Ana Carla P. and Ragni, Mirco},
Booktitle = {Computational Science and Its Applications - ICCSA 2014},
Publisher = {Springer Berlin Heidelberg},
Year = {2014},
Pages = {508-521},
Series = {Lecture Notes in Computer Science},
Volume = {8579},
Archiveprefix = {arXiv},
Doi = {10.1007/978-3-319-09144-0_35},
Eprint = {1410.1073},
Journal = {Lecture Notes in Computer Science},
Primaryclass = {quant-ph},
}
```