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Canonical “Loop” Quantum Gravity and Spin Foam Models

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Recent Developments in General Relativity

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Abstract

The canonical “loop” formulation of quantum gravity is a mathematically well defined, background independent, non-perturbative standard quantization of Einstein’s theory of General Relativity. Some of the most meaningful results of the theory are: 1) the complete calculation of the spectrum of geometric quantities like area and volume and the consequent physical predictions about the structure of space-time at the Planck scale; 2) a microscopical derivation of the Bekenstein-Hawking black-hole entropy formula. Unfortunately, despite recent results, the dynamical aspect of the theory (imposition of the Weller-De Witt constraint) remains elusive.

After a short description of the basic ideas and the main results of loop quantum gravity we show in which sense the exponential of the super-Hamiltonian constraint leads to the concept of spin foam and to a four dimensional formulation of the theory. Moreover, we show that some topological field theories as the BF theory in 3 and 4 dimensions admits a spin foam formulation. We argue that the spin-foam/spin-network formalism it is the natural framework in which to discuss loop quantum gravity and topological field theory.

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Authors
  1. R. De Pietri
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Editors and Affiliations

  1. Dipartimento Interuniversitario di Matematica, Università di Bari, Bari, Italy

    B. Casciaro  & D. Fortunato  & 

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

    M. Francaviglia

  3. Dipartimento Interuniversitario, Politecnico di Bari, Bari, Italy

    A. Masiello

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© 2000 Springer-Verlag Italia

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De Pietri, R. (2000). Canonical “Loop” Quantum Gravity and Spin Foam Models. In: Casciaro, B., Fortunato, D., Francaviglia, M., Masiello, A. (eds) Recent Developments in General Relativity. Springer, Milano. https://doi.org/10.1007/978-88-470-2113-6_6

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  • DOI: https://doi.org/10.1007/978-88-470-2113-6_6

  • Publisher Name: Springer, Milano

  • Print ISBN: 978-88-470-0068-1

  • Online ISBN: 978-88-470-2113-6

  • eBook Packages: Springer Book Archive

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