Spin Foams and Canonical Quantization

Abstract

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. In the three-dimensional context, where the two approaches are in good agreement, we show how the canonical quantization à la Witten of Riemannian gravity with a positive cosmological constant is related to the Turaev-Viro spin foam model, and how the Ponzano-Regge amplitudes are related to the physical scalar product of Riemannian loop quantum gravity without cosmological constant. In the four-dimensional case, we recall a Lorentz-covariant formulation of loop quantum gravity using projected spin networks, compare it with the new spin foam models, and identify interesting relations and their pitfalls. Finally, we discuss the properties which a spin foam model is expected to possess in order to be consistent with the canonical quantization, and suggest a new model illustrating these results.

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Cited by in corpus (36)

• The Spin Foam Approach to Quantum Gravity
• Quantum Cosmology from Group Field Theory Condensates: a Review
• Flowing in Group Field Theory Space: a Review
• A new vacuum for Loop Quantum Gravity
• Towards a phase diagram for spin foams
• The twistorial structure of loop-gravity transition amplitudes
• $BF$ gravity
• Quantum group spin nets: refinement limit and relation to spin foams
• Symmetries of quantum space-time in 3 dimensions
• Quantum gravity kinematics from extended TQFTs
• Discrete Gravity Models and Loop Quantum Gravity: a Short Review
• Geometric temperature and entropy of quantum isolated horizons
• Asymptotic analysis of the EPRL model with timelike tetrahedra
• Chiral description of ghost-free massive gravity
• On the Relations between Gravity and BF Theories
• Flux formulation of loop quantum gravity: Classical framework
• Turaev-Viro amplitudes from 2+1 Loop Quantum Gravity
• Group Field Theory in dimension four minus epsilon
• An elementary introduction to loop quantum gravity
• Testing the role of the Barbero-Immirzi parameter and the choice of connection in Loop Quantum Gravity
• Testing the imposition of the Spin Foam Simplicity Constraints
• Quantization of systems with temporally varying discretization I: Evolving Hilbert spaces
• Holonomy Spin Foam Models: Boundary Hilbert spaces and Time Evolution Operators
• Manifestly Lorentz-covariant variables for the phase space of general relativity
• Quantum geometry from higher gauge theory
• Hamiltonian spinfoam gravity
• Continuous point symmetries in Group Field Theories
• BTZ Black Hole Entropy and the Turaev-Viro model
• Degenerate Plebanski Sector and Spin Foam Quantization
• Towards self dual Loop Quantum Gravity
• Asymptotic Analysis of the Ponzano-Regge Model with Non-Commutative Metric Boundary Data
• Canonical structure of minimal varying $\Lambda$ theories
• Canonical analysis with no second-class constraints of $BF$ gravity with Immirzi parameter
• Aspects of quantum gravity
• Quantum field theoretic representation of Wilson surfaces: II higher topological coadjoint orbit model
• Canonical analysis of $BF$ gravity in $n$ dimensions