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This review is devoted to the analysis of the mutual consistency of the spin foam and canonical loop quantizations in three and four spacetime dimensions.
1915
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Cianfrani F., Montani G., Towards loop quantum gravity without the time gauge,
1916
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Conrady F., Hnybida J., A spin foam model for general Lorentzian 4-geometries,
1959
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Geiller M., Noui K., Testing the imposition of the spin foam simplicity constraints,
1965
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Ponzano G., Regge T., Semiclassical limit of Racah coefficients, in Spectroscopy and Group Theoretical Methods in Physics, Editors F. Block et al., North Holland, Amsterdam, 1968, 1–58
1968
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Plebanski J.F., On the separation of Einsteinian substructures,
1977
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Balachandran A.P., Marmo G., Skagerstam B.S., Stern A., Gauge symmetries and fibre bundles: applications to particle dynamics,
1983
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Deser S., Jackiw R., Three-dimensional cosmological gravity: dynamics of constant curvature,
1984
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Deser S., Jackiw R., ’t Hooft G., Three-dimensional Einstein gravity: dynamics of flat space,
1984
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Goldman W.M., The symplectic nature of fundamental groups of surfaces,
1984
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Freyd P., Yetter D., Hoste J., Lickorish W.B.R., Millett K., Ocneanu A., A new polynomial invariant of knots and links,
1985
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Jones V.F.R., A new knot polynomial and von Neumann algebras,
1986
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Witten E.,
1988
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Elitzur S., Moore G., Schwimmer A., Seiberg N., Remarks on the canonical quantization of the Chern–Simons–Witten theory,
1989
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Horowitz G.T., Exactly soluble diffeomorphism invariant theories,
1989
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Labastida J.M.F., Ramallo A.V., Operator formalism for Chern–Simons theories,
1989
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Witten E., Quantum field theory and the Jones polynomial,
1989
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de Sousa Gerbert P., On spin and (quantum) gravity in
1990
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Vassiliev V.A., Cohomology of knot spaces, in Theory of Singularities and its Applications,
1990
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Capovilla R., Dell J., Jacobson T., Mason L., Self-dual
1991
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Gott III J.R., Closed timelike curves produced by pairs of moving cosmic strings: exact solutions,
1991
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Reshetikhin N., Turaev V.G., Invariants of
1991
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Marolf D.M., Loop representations for
1993
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Ashtekar A., Loll R., New loop representations for
1994
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Henneaux M., Slavnov A.A., A note on the path integral for systems with primary and secondary second class constraints,
1994
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Alekseev A.Y., Integrability in the Hamiltonian Chern–Simons theory,
1995
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Alekseev A.Y., Grosse H., Schomerus V., Combinatorial quantization of the Hamiltonian Chern–Simons theory. I,
1995
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Chari V., Pressley A., A guide to quantum groups, Cambridge University Press, Cambridge, 1995
1995
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Foxon T.J., Spin networks, Turaev–Viro theory and the loop representation,
1995
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Giulini D., On the configuration space topology in general relativity,
1995
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Rovelli C., Smolin L., Discreteness of area and volume in quantum gravity,
1995
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Alekseev A.Y., Grosse H., Schomerus V., Combinatorial quantization of the Hamiltonian Chern–Simons theory. II,
1996
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Alekseev A.Y., Schomerus V., Representation theory of Chern–Simons observables,
1996
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Grot N., Rovelli C., Moduli-space structure of knots with intersections,
1996
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Holst S., Barbero’s Hamiltonian derived from a generalized Hilbert–Palatini action,
1996
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Ashtekar A., Lewandowski J., Quantum theory of geometry. I. Area operators,
1997
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Ashtekar A., Lewandowski J., Quantum theory of geometry. II. Volume operators,
1997
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Koornwinder T.H., Muller N.M., The quantum double of a (locally) compact group,
1997
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Reisenberger M.P., Rovelli C., “Sum over surfaces” form of loop quantum gravity,
1997
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Alexandrov S.Y., Vassilevich D.V., Path integral for the Hilbert–Palatini and Ashtekar gravity,
1998
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Barrett J.W., Crane L., Relativistic spin networks and quantum gravity,
1998
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Carlip S., Quantum gravity in
1998
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Koornwinder T.H., Bais F.A., Muller N.M., Tensor product representations of the quantum double of a compact group,
1998
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Thiemann T., A length operator for canonical quantum gravity,
1998
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De Pietri R., Freidel L.,
1999
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Fock V.V., Rosly A.A., Poisson structure on moduli of flat connections on Riemann surfaces and the
1999
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Freidel L., Krasnov K., Puzio R., BF description of higher-dimensional gravity theories,
1999
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Alexandrov S.,
2000
Cited alongside, same era.
Barrett J.W., Crane L., A Lorentzian signature model for quantum general relativity,
2000
Cited alongside, same era.
Samuel J., Is Barbero’s Hamiltonian formulation a gauge theory of Lorentzian gravity?,
2000
Cited alongside, same era.
Alexandrov S., Vassilevich D., Area spectrum in Lorentz covariant loop gravity,
2001
Cited alongside, same era.
Barros e Sá N., Hamiltonian analysis of general relativity with the Immirzi parameter,
2001
Cited alongside, same era.
Crane L., Perez A., Rovelli C., Perturbative finiteness in spin-foam quantum gravity,
2001
Cited alongside, same era.
Alexandrov S., Spin foam model from canonical quantization,
2008
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Conrady F., Freidel L., Semiclassical limit of 4-dimensional spin foam models,
2008
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Engle J., Livine E., Pereira R., Rovelli C., LQG vertex with finite Immirzi parameter,
2008
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Engle J., Pereira R., Rovelli C., Flipped spinfoam vertex and loop gravity,
2008
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Freidel L., Krasnov K., A new spin foam model for 4D gravity,
2008
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Labastida J.M.F., Knot invariants and Chern–Simons theory, in European Congress of Mathematics, Vol. II (Barcelona, 2000),
2001
Cited alongside, same era.
Matschull H.J., The phase space structure of multi-particle models in
2001
Cited alongside, same era.
Perez A., Finiteness of a spinfoam model for Euclidean quantum general relativity,
2001
Cited alongside, same era.
Perez A., Rovelli C.,
2001
Cited alongside, same era.
Perez A., Rovelli C., A spin foam model without bubble divergences,
2001
Cited alongside, same era.
Perez A., Rovelli C., Spin foam model for Lorentzian general relativity,
2001
Cited alongside, same era.
Later among the works it cites.
2009
Later among the works it cites.
2009
Later among the works it cites.
Barrett J.W., Naish-Guzman I., The Ponzano–Regge model,
2009
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Bianchi E., The length operator in loop quantum gravity,
2009
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Bonzom V., From lattice BF gauge theory to areaangle Regge calculus,
2009
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2009
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Joung E., Mourad J., Noui K., Three dimensional quantum geometry and deformed symmetry,
2009
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Livine E.R., Ryan J.P., A note on B-observables in Ponzano–Regge 3D quantum gravity,
2009
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2009
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Alexandrov S., New vertices and canonical quantization,
2010
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Baratin A., Oriti D., Group field theory with noncommutative metric variables,
2010
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2010
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Bojowald M., Perez A., Spin foam quantization and anomalies,
2010
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Bonzom V., Smerlak M., Bubble divergences from cellular cohomology,
2010
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2010
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Dupuis M., Livine E.R., Lifting SU(2) spin networks to projected spin networks,
2010
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2010
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2010
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Kamiński W., Kisielowski M., Lewandowski J., The EPRL intertwiners and corrected partition function,
2010
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Liu L., Montesinos M., Perez A., Topological limit of gravity admitting an
2010
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Meusburger C., Noui K., Combinatorial quantisation of the Euclidean torus universe,
2010
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Perez A., Pranzetti D., On the regularization of the constraint algebra of quantum gravity in
2010
Later among the works it cites.
Alexandrov S., Roche P., Critical overview of loops and foams,
2011
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2011
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2011
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Bonzom V., Spin foam models and the Wheeler–DeWitt equation for the quantum 4-simplex,
2011
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Bonzom V., Freidel L., The Hamiltonian constraint in 3d Riemannian loop quantum gravity,
2011
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Geiller M., Lachièze-Rey M., Noui K., A new look at Lorentz-covariant loop quantum gravity,
2011
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2011
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Han M., 4-dimensional spin-foam model with quantum Lorentz group,
2011
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Noui K., Perez A., Pranzetti D., Canonical quantization of non-commutative holonomies in
2011
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Rovelli C., Speziale S., Lorentz covariance of loop quantum gravity,
2011
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Sahlmann H., Thiemann T., Chern–Simons theory, Stokes’ theorem, and the Duflo map,
2011
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2011
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Bonzom V., Laddha A., Lessons from toy-models for the dynamics of loop quantum gravity,
2012
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Bonzom V., Smerlak M., Bubble divergences from twisted cohomology,
2012
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Bonzom V., Smerlak M., Bubble divergences: sorting out topology from cell structure,
2012
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Fairbairn W.J., Meusburger C., Quantum deformation of two four-dimensional spin foam models,
2012
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Mikovic A., Vojinovic M., Effective action for EPRL/FK spin foam models,
2012
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Reisenberger M.P., On relativistic spin network vertices,
2054
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Freidel L., Livine E.R., Ponzano–Regge model revisited. III. Feynman diagrams and effective field theory,
2061
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