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Combinatorial and Geometrical Origins of Regge Symmetries: Their Manifestations from Spin-Networks to Classical Mechanisms, and Beyond

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Computational Science and Its Applications – ICCSA 2017 (ICCSA 2017)

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Abstract

Tullio Regge discovered new symmetries in 1958, hidden in formulas for calculations of the coupling and recoupling coefficients of quantum angular momentum theory, as developed principally by Wigner and Racah: the only known (limited) application appeared computational. Ten years later, in a paper with Ponzano, Regge provided a semiclassical interpretation showing relevance to the basic geometry of quadrilaterals and tetrahedra, and opening also a promising road to quantum gravity, still currently being explored. New facets are here indicated, continuing a sequence of papers in this Lecture Notes series and elsewhere. We emphasize how an integrated combinatorial and geometrical interpretation is emerging, and also examples from the quantum mechanics of atoms and molecules are briefly documented. Attention is dedicated to the recently pointed out connection between the quantum mechanics of spin recouplings and the Grashof analysis of four-bar linkages, with perspective implications at the molecular level.

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Acknowledgments

Robenilson Ferreira is grateful to Brazilian CAPES for a sandwich doctoral (PDSE88881.134388/2016-01) fellowship to the Perugia University. Manuela Arruda is grateful to Brazilian CNPq (Conselho Nacional de Desenvolvimento Científico e Tecnológico) for a post doctoral fellowship to the Perugia University. Vincenzo Aquilanti and Frederico Vasconcellos Prudente thank Brazilian CAPES for a Special Visiting Professorship at the Bahia Federal University (PVE 027/2013) and the Italian MIUR for Grant SIR 2014 (RBSI14U3VF).

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Authors and Affiliations

  1. Dipartimento di Chimica, Biologia e Biotecnologie, Università di Perugia, via Elce di Sotto, 8, 06183, Perugia, Italy

    Vincenzo Aquilanti

  2. Consiglio Nazionale Delle Ricerche, Piazzale Aldo Moro 7, 00185, Rome, Italy

    Vincenzo Aquilanti

  3. Centro de Ciências Exatas e Tecnológicas, Universidade Federal do Recôncavo da Bahia, Rua Rui Barbosa 710, Cruz Das Almas, BA, 44380-000, Brazil

    Manuela S. Arruda

  4. Dipartimento di Farmacia, Università G. d’Annunzio, Via Dei Vestini, 66100, Chieti, Italy

    Cecilia Coletti

  5. Department of Physics, University of California, Berkeley, CA, 94720-7300, USA

    Robert Littlejohn

  6. Instituto de Física, Universidade Federal da Bahia, Campus Universitario de Ondina, Salvador, BA, 40170-115, Brazil

    Robenilson F. Santos

  7. Instituto Federal de Alagoas, Campus Piranhas, Avenida Sergipe s/n, Piranhas, AL, 57460-000, Brazil

    Robenilson F. Santos

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  1. Vincenzo Aquilanti
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  3. Cecilia Coletti
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  4. Robert Littlejohn
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  5. Robenilson F. Santos
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Correspondence to Cecilia Coletti .

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Editors and Affiliations

  1. University of Perugia, Perugia, Italy

    Osvaldo Gervasi

  2. University of Basilicata, Potenza, Italy

    Beniamino Murgante

  3. Covenant University, Ota, Nigeria

    Sanjay Misra

  4. University of Trieste, Trieste, Italy

    Giuseppe Borruso

  5. Polytechnic University of Bari, Bari, Italy

    Carmelo M. Torre

  6. University of Minho, Braga, Portugal

    Ana Maria A.C. Rocha

  7. Monash University, Clayton, Victoria, Australia

    David Taniar

  8. Kyushu Sangyo University, Fukuoka, Japan

    Bernady O. Apduhan

  9. Saint Petersburg State University, Saint Petersburg, Russia

    Elena Stankova

  10. University of Trieste, Trieste, Italy

    Alfredo Cuzzocrea

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Aquilanti, V., Arruda, M.S., Coletti, C., Littlejohn, R., Santos, R.F. (2017). Combinatorial and Geometrical Origins of Regge Symmetries: Their Manifestations from Spin-Networks to Classical Mechanisms, and Beyond. In: Gervasi, O., et al. Computational Science and Its Applications – ICCSA 2017. ICCSA 2017. Lecture Notes in Computer Science(), vol 10408. Springer, Cham. https://doi.org/10.1007/978-3-319-62404-4_23

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