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

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Cited by in corpus (40)

• The Spin Foam Approach to Quantum Gravity
• LQG vertex with finite Immirzi parameter
• A New Spin Foam Model for 4d Gravity
• Lorentzian spin foam amplitudes: graphical calculus and asymptotics
• Flipped spinfoam vertex and loop gravity
• The complete LQG propagator: I. Difficulties with the Barrett-Crane vertex
• Group field theory and simplicial gravity path integrals: A model for Holst-Plebanski gravity
• Consistently Solving the Simplicity Constraints for Spinfoam Quantum Gravity
• Edge modes of gravity -- II: Corner metric and Lorentz charges
• Edge modes of gravity. Part III. Corner simplicity constraints
• The complete LQG propagator: II. Asymptotic behavior of the vertex
• Lorentz covariance of loop quantum gravity
• Simplicity in simplicial phase space
• Spin Foams and Canonical Quantization
• Lorentzian LQG vertex amplitude
• Lifting SU(2) Spin Networks to Projected Spin Networks
• The new vertices and canonical quantization
• Simplicity and closure constraints in spin foam models of gravity
• A proposed proper EPRL vertex amplitude
• Critical Overview of Loops and Foams
• A Lagrangian approach to the Barrett-Crane spin foam model
• The Holst Spin Foam Model via Cubulations
• Towards the graviton from spinfoams: the complete perturbative expansion of the 3d toy model
• The perturbative Regge-calculus regime of Loop Quantum Gravity
• Coherent states, constraint classes, and area operators in the new spin-foam models
• First order gravity on the light front
• Testing the imposition of the Spin Foam Simplicity Constraints
• Revisiting the Simplicity Constraints and Coherent Intertwiners
• Numerical indications on the semiclassical limit of the flipped vertex
• Polytopes in all dimensional loop quantum gravity
• The Plebanski sectors of the EPRL vertex
• Encoding simplicial quantum geometry in group field theories
• Spinfoams: Foundations
• Intertwiner dynamics in the flipped vertex
• The new spin foam models and quantum gravity
• A Short and Subjective Introduction to the Spinfoam Framework for Quantum Gravity
• Tensorial Structure of the LQG graviton propagator
• Degenerate Plebanski Sector and Spin Foam Quantization
• Poincare-Plebanski formulation of GR and dual simplicity constraints
• On Geometry and Symmetries in Classical and Quantum Theories of Gauge Gravity