A new spinfoam vertex for quantum gravity

Abstract

We introduce a new spinfoam vertex to be used in models of 4d quantum gravity based on SU(2) and SO(4) BF theory plus constraints. It can be seen as the conventional vertex of SU(2) BF theory, the 15j symbol, in a particular basis constructed using SU(2) coherent states. This basis makes the geometric interpretation of the variables transparent: they are the vectors normal to the triangles within each tetrahedron. We study the condition under which these states can be considered semiclassical, and we show that the semiclassical ones dominate the evaluation of quantum correlations. Finally, we describe how the constraints reducing BF to gravity can be directly written in terms of the new variables, and how the semiclassicality of the states might improve understanding the correct way to implement the constraints.

17+8 pages, 6 figures. v2 updated references

References in corpus (2)

• Loop quantum cosmology of k=1 FRW models
• The loop-quantum-gravity vertex-amplitude

Cited by in corpus (14)

• LQG vertex with finite Immirzi parameter
• A New Spin Foam Model for 4d Gravity
• Flipped spinfoam vertex and loop gravity
• The complete LQG propagator: I. Difficulties with the Barrett-Crane vertex
• Area-angle variables for general relativity
• The complete LQG propagator: II. Asymptotic behavior of the vertex
• Spin foam model from canonical quantization
• Simplicity and closure constraints in spin foam models of gravity
• The perturbative Regge-calculus regime of Loop Quantum Gravity
• Coherent states, constraint classes, and area operators in the new spin-foam models
• A New Class of Group Field Theories for 1st Order Discrete Quantum Gravity
• Spin-Foam Models and the Physical Scalar Product
• Numerical indications on the semiclassical limit of the flipped vertex
• Physical boundary state for the quantum tetrahedron