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2010

Lifting SU(2) Spin Networks to Projected Spin Networks

Dupuis, Maité, Livine, Etera R.

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Projected spin network states are the canonical basis of quantum states of geometry for the most recent EPR-FK spinfoam models for quantum gravity.

They are functionals of both the Lorentz connection and the time normal field.
We analyze in details the map from these projected spin networks to the standard SU(2) spin networks of loop quantum gravity.
We show that this map is not one-to-one and that the corresponding ambiguity is parameterized by the Immirzi parameter.

Lifting SU(2) Spin Networks to Projected Spin Networks · Around

Built on

E.R. Livine and S. Speziale, Consistently Solving the Simplicity Constraints for Spinfoam Quantum Gravity
Original
1915
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A. Ashtekar and J. Lewandowski, Projective Techniques and Functional Integration
1995
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J.W. Barrett and L. Crane, A Lorentzian Signature Model for Quantum General Relativity
2000
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S. Alexandrov and D. Vassilevich, Area spectrum in Lorentz covariant loop gravity
2001
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A. Perez and C. Rovelli, Spin foam model for Lorentzian General Relativity
2001
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S. Alexandrov, Hilbert space structure of covariant loop quantum gravity
2002
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E.R. Livine, Projected Spin Networks for Lorentz connection: Linking Spin Foams and Loop Gravity
2002
Earlier work this paper cites.

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