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U(N) Coherent States for Loop Quantum Gravity · Around

2010

U(N) Coherent States for Loop Quantum Gravity

Freidel, Laurent, Livine, Etera R.

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We investigate the geometry of the space of N-valent SU(2)-intertwiners.

We propose a new set of holomorphic operators acting on this space and a new set of coherent states which are covariant under U(N) transformations.
These states are labeled by elements of the Grassmannian Gr(N,2), they possess a direct geometrical interpretation in terms of framed polyhedra and are shown to be related to the well-known coherent intertwiners.

Built on

E.R. Livine and S. Speziale, Consistently Solving the Simplicity Constraints for Spinfoam Quantum Gravity
Original
1915
Earlier work this paper cites.
J. Hoppe, Diffeomorphism Groups, Quantization, and SU ⁡ ( ∞ ) \mathrm{SU}(\infty)
1989
Earlier work this paper cites.
F. Girelli and E.R. Livine, Reconstructing Quantum Geometry from Quantum Information: Spin Networks as Harmonic Oscillators
2005
Earlier work this paper cites.

Similar

E.R. Livine and S. Speziale, A new spinfoam vertex for quantum gravity
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J. Engle, E. Livine, R. Pereira and C. Rovelli, LQG vertex with finite Immirzi parameter
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L. Freidel and K. Krasnov, A New Spin Foam Model for 4d Gravity
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L. Freidel and E.R. Livine, The Fine Structure of SU(2) Intertwiners from U(N) Representations
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F. Conrady and L. Freidel, Quantum geometry from phase space reduction
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L. Freidel, K. Krasnov and E.R. Livine, Holomorphic Factorization for a Quantum Tetrahedron
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L. Freidel and S. Speziale, Twisted geometries: A geometric parametrisation of SU(2) phase space
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L. Freidel and E.R. Livine, Generalized Holonomy Operators for Loop Quantum Gravity
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Then

F. Conrady and L. Freidel, On the semiclassical limit of 4d spin foam models
Original
2008
Later among the works it cites.
L. Freidel and E.R. Livine, Ponzano-Regge model revisited III: Feynman diagrams and Effective field theory
Original
2009
Later among the works it cites.

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