Spin foam quantization and anomalies (original) (raw)

• Perez A.: Spin foam models for quantum gravity. Class. Quant. Grav. 20, R43 (2003)
  Article MATH ADS Google Scholar
• Oriti D.: Spacetime geometry from algebra: spin foam models for non-perturbative quantum gravity. Rept. Prog. Phys. 64, 1489–1544 (2001)
  Article MathSciNet ADS Google Scholar
• Noui K., Perez A.: Three dimensional loop quantum gravity: Physical scalar product and spin foam models. Class. Quant. Gravit. 22, 1739 (2005)
  Article MATH MathSciNet ADS Google Scholar
• Perez A.: Spinfoam quantization of SO(4) Plebanski’s action. Adv. Theor. Math. Phys. 5, 947–968 (2001)
  MATH MathSciNet Google Scholar
• Plebanski J.F.: On the separation of Einsteinian substructures. J. Math. Phys. 18, 2511 (1977)
  Article MATH MathSciNet ADS Google Scholar
• Thiemann T.: Anomaly-free formulation of non perturbative, four dimensional Lorentzian quantum gravity. Phys. Lett. B 380, 257 (1996)
  Article MATH MathSciNet ADS Google Scholar
• Freidel L., Louapre D.: Diffeomorphisms and spin foam models. Nucl. Phys. B 662, 279–298 (2003)
  Article MATH MathSciNet ADS Google Scholar
• Freidel L., Louapre D.: Ponzano–Regge model revisited. I: Gauge fixing, observables and interacting spinning particles. Class. Quant. Gravit. 21, 5685 (2004) [arXiv:hep-th/0401076]
  Article MATH MathSciNet ADS Google Scholar
• Thiemann T.: QSD V: quantum gravity as the natural regulator of matter quantum field theories. Class. Quant. Gravit. 15, 1281–1314 (1998)
  Article MATH MathSciNet ADS Google Scholar
• Reisenberger M.P., Rovelli C.: Spacetime as a Feynman diagram: the connection formulation. Class. Quant. Gravit. 18, 121–140 (2001)
  Article MATH MathSciNet ADS Google Scholar
• Perez A., Rovelli C.: A spin foam model without bubble divergences. Nucl. Phys. B 599, 255–282 (2001)
  Article MATH MathSciNet ADS Google Scholar
• Baez J.C.: An introduction to spin foam models of quantum gravity and BF theory. Lect. Notes Phys. 543, 25–94 (2000)
  Article MathSciNet ADS Google Scholar
• Crane, L., Yetter, D.: A categorical construction of 4-D topological quantum field theories. In: Kaufmann, L., Baadhio, R. (eds.) Quantum Topology, World Scientific, Singapore (1993)
• Reisenberger, M.P.: A lattice worldsheet sum for 4-D Euclidean general relativity. Preprint gr-qc/ 9711052 (1997)
• Barrett J.W., Crane L.: Relativistic spin networks and quantum gravity. J. Math. Phys. 39, 3296–3302 (1998)
  Article MATH MathSciNet ADS Google Scholar
• Barrett J.W., Crane L.: A Lorentzian signature model for quantum general relativity. Class. Quant. Gravit. 17, 3101–3118 (2000)
  Article MATH MathSciNet ADS Google Scholar
• Perez A.: Finiteness of a spinfoam model for Euclidean quantum general relativity. Nucl. Phys. B 599, 427–434 (2001)
  Article MATH ADS Google Scholar
• Crane, L., Perez, A., Rovelli, C.: A finiteness proof for the Lorentzian state sum spin foam model for quantum general relativity. Preprint gr-qc/0104057 (2001)
• Crane L., Perez A., Rovelli C.: Perturbative finiteness in spin-foam quantum gravity. Phys. Rev. Lett. 87, 181301 (2001)
  Article MathSciNet ADS Google Scholar
• Baez J.C., Christensen J.D.: Spin foam models of Riemannian quantum gravity. Class. Quant. Gravit. 19, 4627–4648 (2002)
  Article MATH MathSciNet ADS Google Scholar
• Girelli F., Oeckl R., Perez A.: Spin Foam Diagrammatics and Topological Invariance. Class. Quant. Gravit. 19, 1093–1108 (2002)
  Article MATH MathSciNet ADS Google Scholar
• Bojowald M., Strobl T.: Poisson geometry in constrained systems. Rev. Math. Phys. 15, 663–703 (2003)
  Article MATH MathSciNet Google Scholar
• Faddeev L.D.: Theor. Math. Phys 1, 1 (1969)
• Alekseev A.Y., Schomerus V., Strobl T.: Closed constraint algebras and path integrals for loop group actions. J. Math. Phys. 42, 2144–2155 (2001)
  Article MATH MathSciNet ADS Google Scholar
• Henneaux M., Slavnov A.: A note on the path integral for systems with primary and secondary second class constraints. Phys. Lett. B 338, 47–50 (1994)
  Article MathSciNet ADS Google Scholar
• Buffenoir E., Henneaux M., Noui K., Roche P.: Hamiltonian analysis of Plebanski theory. Class. Quant. Gravit. 21, 5203 (2004)
  Article MATH MathSciNet ADS Google Scholar
• Gambini R., Pullin J.: Canonical quantization of general relativity in discrete spacetimes. Phys. Rev. Lett. 90, 021301 (2003)
  Article MathSciNet ADS Google Scholar
• Di Bartolo C., Gambini R., Pullin J.: Canonical quantization of constrained theories on discrete space–time lattices. Class. Quant. Gravit. 19, 5275–5296 (2002)
  Article MATH MathSciNet Google Scholar
• Thiemann, T.: Introduction to modern canonical quantum general relativity. Preprint gr-qc/0110034 (2001)
• Baez J.C.: Spin foam models. Class. Quant. Gravit. 15, 1827–1858 (1998)
  Article MATH MathSciNet ADS Google Scholar
• Husain V., Kuchař K.V.: General covariance, new variables and dynamics without dynamics. Phys. Rev. D 42, 4070–4077 (1990)
  Article MathSciNet ADS Google Scholar
• Montesinos, M., Velazquez M.: Husain–Kuchar model as a constrained BF theory. arXiv:0812.2825 [gr-qc]
• Zapata, J.A.: A combinatorial approach to quantum gauge theories and quantum gravity. Preprint UMI-99-01167 (1999)
• Zapata J.A.: Continuum spin foam model for 3D gravity. J. Math. Phys. 43, 5612–5623 (2002)
  Article MATH MathSciNet ADS Google Scholar
• Reisenberger M.P., Rovelli C.: “Sum over surfaces” form of loop quantum gravity. Phys. Rev. D 56, 3490–3508 (1997)
  Article MathSciNet ADS Google Scholar
• Gaul M., Rovelli C.: A generalized Hamiltonian constraint operator in loop quantum gravity and its simplest Euclidean matrix elements. Class. Quant. Gravit. 18, 1593–1624 (2001)
  Article MATH MathSciNet ADS Google Scholar
• Perez A., Rovelli C.: Spin foam model for Lorentzian general relativity. Phys. Rev. D 63, 041501 (2001)
  Article MathSciNet ADS Google Scholar
• De Pietri R., Freidel L., Krasnov K., Rovelli C.: Barrett–Crane model from a Boulatov–Ooguri field theory over a homogeneous space. Nucl. Phys. B 574, 785–806 (2000)
  Article MATH MathSciNet ADS Google Scholar
• Klauder J.: Coherent state quantization of constraint systems. Ann. Phys. 254, 419 (1997)
  Article MATH MathSciNet ADS Google Scholar
• Klauder J.: Universal procedure for enforcing quantum constraints. Nucl. Phys. B 547, 397–412 (1999)
  Article MATH MathSciNet ADS Google Scholar
• Klauder, J.: Quantization of constrained systems. Lect. Notes Phys., vol. 572, pp. 143–182. In: Proceedings of 39th Internationale Universitätswochen für Kern- und Teilchenphysik (International University Weeks of Nuclear and Particle Physics): Methods of Quantization (IUKT 39), Schladming, Austria, 26 Feb–4 Mar 2000 (2001)
• Reisenberger, M.P.: Classical Euclidean general relativity from “left-handed area = right-handed area. Preprint gr-qc/9804061 (1998)