The new vertices and canonical quantization

Abstract

We present two results on the recently proposed new spin foam models. First, we show how a (slightly modified) restriction on representations in the EPRL model leads to the appearance of the Ashtekar-Barbero connection, thus bringing this model even closer to LQG. Second, we however argue that the quantization procedure used to derive the new models is inconsistent since it relies on the symplectic structure of the unconstraint BF theory.

16 pages, 1 figure; added subsection on ordering of Casimir operators, more details on imposing simplicity constraints

References in corpus (8)

• LQG vertex with finite Immirzi parameter
• A new spinfoam vertex for quantum gravity
• A New Spin Foam Model for 4d Gravity
• A spin foam model for general Lorentzian 4-geometries
• Spin foam model from canonical quantization
• Simplicity and closure constraints in spin foam models of gravity
• Plebanski Theory and Covariant Canonical Formulation
• Spin foams with timelike surfaces

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• The twistorial structure of loop-gravity transition amplitudes
• A high-performance code for EPRL spin foam amplitudes
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• Two-point functions in (loop) quantum cosmology
• Holonomy Spin Foam Models: Boundary Hilbert spaces and Time Evolution Operators
• Renormalization of a tensorial field theory on the homogeneous space SU(2)/U(1)
• Spinfoams: Foundations
• The new spin foam models and quantum gravity
• Degenerate Plebanski Sector and Spin Foam Quantization
• Poincare-Plebanski formulation of GR and dual simplicity constraints
• Equivalent and Alternative Forms for BF Gravity with Immirzi Parameter
• The kinematical Hilbert space of Loop Quantum Gravity from BF theories
• On Geometry and Symmetries in Classical and Quantum Theories of Gauge Gravity
• New insights in quantum geometry
• The relation between Geometry and Matter in classical and quantum Gravity and Cosmology
• SU(2) gauge symmetry in gravity phase space