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Symmetric Angular Momentum Coupling, the Quantum Volume Operator and the 7-spin Network: A Computational Perspective

2014; Springer Science+Business Media; Linguagem: Inglês

10.1007/978-3-319-09144-0_35

1611-3349

Dimitri Marinelli, Annalisa Marzuoli, Vincenz̊o Aquilanti, Roger W. Anderson, Ana Carla P. Bitencourt, Mirco Ragni,

Quantum Chromodynamics and Particle Interactions

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 Wigner’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.