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

Autor:	Borja, Enrique F., Diaz-Polo, Jacobo, Garay, Iñaki
Rok vydání:	2011
Předmět:	General Relativity and Quantum Cosmology
Druh dokumentu:	Working Paper
Popis:	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. Comment: 16 pages. Proceedings for the 3rd Quantum Geometry and Quantum Gravity School in Zakopane (2011)
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1110.4578 Zobrazit plný text záznamu View this record from Arxiv