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Spin Models, TQFTs and Their Hierarchical Structure

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Book cover Recent Developments in General Relativity, Genoa 2000

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Abstract

State sum models based on the recoupling theory of SU(2) angular momenta can be defined in any dimension d, and the corresponding hierarchy includes the Ponzano-Regge model in d = 3 and the Crane-Yetter invariant in d = 4. Here we establish an equivalence between each of these spin models and a corresponding B F theory by exploiting suitable d-dimensional generalizations of the Ooguri’s approach in d = 3.

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References

  1. Birmingham, D., Blau, I., Rakowski, M., Thomson, G. (1991): Phys. Rep. 209, 129

    Article  MathSciNet  ADS  Google Scholar 

  2. Carbone, G., Carfora, M., Marzuoli, A. (2001): Nucl. Phys. B 595 [PM], 654

    Article  MathSciNet  ADS  Google Scholar 

  3. Ponzano, G., Regge, T. (1968): Semiclassical limit of Racah coefficients, in Spectroscopic and Group Theoretical Methods in Physics, ed. by F. Bloch, S.G. Cohen, A. De Shalit, S. Sambursky, I. Talmi, North-Holland Publ. Co., Amsterdam, p. 1

    Google Scholar 

  4. Crane, L., Kauffman, L.H., Yetter, D.N.: State sum invariants of four manifolds; hep-th/9409167

    Google Scholar 

  5. Ooguri, H. (1992): Nucl. Phys. B 382, 276

    Article  MathSciNet  ADS  Google Scholar 

  6. Broda, B. (1995): A gauge-field approach to 3-and 4-manifold invariants, in Symplectic singularities and geometry of gauge field, ed. by R. Budzynski, S. Janeczk, O.W. Kondracki, A.F. Kunzle, Polish Academy of Science, Warsaw, p. 201

    Google Scholar 

  7. Roberts, J. (1995): Topology 34, 771

    Article  MathSciNet  MATH  Google Scholar 

  8. Carbone, G. (2000): Ph.D Thesis, S.LS.S.A.-I.S.A.S., Trieste

    Google Scholar 

  9. Oriti, D., Williams, R.M. (2001): Phys. Rev. D 63, 024022

    Article  MathSciNet  ADS  Google Scholar 

  10. Freidel, L., Krasnov, K. (1999): Adv. Theor. Math. Phys. 2, 1183

    MathSciNet  Google Scholar 

  11. Yutsis, A.P., Levinson, LB., Vanagas, V.V. (1962): The Mathematical Apparatus of the Theory of Angular Momentum. Published for the National Science Foundation by the Israel Program for Scientific Translation, Jerusalem

    MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. S.I.S.S.A., Via Beirut 2-4, 34014, Trieste, Italy

    G. Carbone

  2. Ecole Normale Supérieure de Lyon, Laboratoire de Physique, Allee d’Italie 46, 6936, Lyon, Cedex 07, France

    G. Carbone

  3. Dipartimento di Fisica Nucleare e Teorica, Università degli Studi di Pavia, and Istituto Nazionale di Fisica Nucleare, Sezione di Pavia, Via A. Bassi 6, 27100, Pavia, Italy

    M. Carfora & A. Marzuoli

Authors
  1. G. Carbone
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  2. M. Carfora
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  3. A. Marzuoli
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Corresponding author

Correspondence to G. Carbone .

Editor information

Editors and Affiliations

  1. Dipartimento di Metodi e Modelli Matematici (DIMET), Università di Genova, Genova, Italy

    R. Cianci

  2. Dipartimento di Fisica, Università di Genova and Istituto Nazionale di Fisica Nucleare, Sezione di Genova, Genova, Italy

    R. Collina

  3. Dipartimento di Matematica, Università di Torino, Torino, Italy

    M. Francaviglia

  4. Dipartimento di Fisica Teorica, Università di Torino and Istituto Nazionale di Fisica Nucleare, Sezione di Torino, Torino, Italy

    P. Fré

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© 2002 Springer-Verlag Italia

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Carbone, G., Carfora, M., Marzuoli, A. (2002). Spin Models, TQFTs and Their Hierarchical Structure. In: Cianci, R., Collina, R., Francaviglia, M., Fré, P. (eds) Recent Developments in General Relativity, Genoa 2000. Springer, Milano. https://doi.org/10.1007/978-88-470-2101-3_40

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  • DOI: https://doi.org/10.1007/978-88-470-2101-3_40

  • Publisher Name: Springer, Milano

  • Print ISBN: 978-88-470-0162-6

  • Online ISBN: 978-88-470-2101-3

  • eBook Packages: Springer Book Archive

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