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U(N) and holomorphic methods for LQG and Spin Foams · Around

2011

U(N) and holomorphic methods for LQG and Spin Foams

Borja, Enrique F., Diaz-Polo, Jacobo, Garay, Iñaki

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The U(N) framework and the spinor representation for loop quantum gravity are two new points of view that can help us deal with the most fundamental problems of the theory.

Here, we review the detailed construction of the U(N) framework explaining how one can endow the Hilbert space of N-leg intertwiners with a Fock structure.
We then give a description of the classical phase space corresponding to this system in terms of the spinors, and we will study its quantization using holomorphic techniques.
We take special care in constructing the usual holonomy operators of LQG in terms of spinors, and in the description of the Hilbert space of LQG with the different polarization given by these spinors.

Built on

Reconstructing quantum geometry from quantum information: Spin networks as harmonic oscillators
Florian Girelli and Etera R. Livine · 2005
Earlier work this paper cites.
The Fine Structure of SU ⁡ ( 2 ) \mathrm{SU}(2) Intertwiners from U ⁡ ( N ) \mathrm{U}(N) Representations
Original
Laurent Freidel and Etera R. Livine · 2010
Earlier work this paper cites.
Dynamics for a 2-vertex Quantum Gravity Model
Original
Enrique F. Borja, Jacobo Diaz-Polo, Iñaki Garay and Etera R. Livine · 2010
Earlier work this paper cites.

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Then

U ⁡ ( N ) \mathrm{U}(N) tools for Loop Quantum Gravity: The Return of the Spinor
Original
Enrique F. Borja, Laurent Freidel, Iñaki Garay and Etera R. Livine · 2011
Closest in time.
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