Projected Spin Networks for Lorentz connection: Linking Spin Foams and Loop Gravity

Details Projected Spin Networks for Lorentz connection: Linking Spin Foams and Loop Gravity Projected Spin Networks for Lorentz connection: Linking Spin Foams and Loop Gravity

2002-07-22

arxiv.org/abs/gr-qc/0207084v1

Class.Quant.Grav. 19 (2002) 5525-5542

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

Latex, 15 pages

Scientific paper

10.1088/0264-9381/19/21/316

In the search for a covariant formulation for Loop Quantum Gravity, spin foams have arised as the corresponding discrete space-time structure and, among the different models, the Barrett-Crane model seems the most promising. Here, we study its boundary states and introduce cylindrical functions on both the Lorentz connection and the time normal to the studied hypersurface. We call them projected cylindrical functions and we explain how they would naturally arise in a covariant formulation of Loop Quantum Gravity.

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