Spin foam model from canonical quantization

Abstract

We suggest a modification of the Barrett-Crane spin foam model of 4-dimensional Lorentzian general relativity motivated by the canonical quantization. The starting point is Lorentz covariant loop quantum gravity. Its kinematical Hilbert space is found as a space of the so-called projected spin networks. These spin networks are identified with the boundary states of a spin foam model and provide a generalization of the unique Barrette-Crane intertwiner. We propose a way to modify the Barrett-Crane quantization procedure to arrive at this generalization: the B field (bi-vectors) should be promoted not to generators of the gauge algebra, but to their certain projection. The modification is also justified by the canonical analysis of Plebanski formulation. Finally, we compare our construction with other proposals to modify the Barret-Crane model.

26 pages; presentation improved, important changes concerning the closure constraint and the vertex amplitude; minor correction

References in corpus (2)

• A new spinfoam vertex for quantum gravity
• The loop-quantum-gravity vertex-amplitude

Cited by in corpus (10)

• 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
• The complete LQG propagator: II. Asymptotic behavior of the vertex
• 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
• Numerical indications on the semiclassical limit of the flipped vertex
• Tensorial Structure of the LQG graviton propagator