Lifting SU(2) Spin Networks to Projected Spin Networks

Details Lifting SU(2) Spin Networks to Projected Spin Networks Lifting SU(2) Spin Networks to Projected Spin Networks

2010-08-24

arxiv.org/abs/1008.4093v1

Phys. Rev. D 82, 064044 (2010)

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

14 pages

Scientific paper

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. We conclude with a comparison of the scalar products between projected spin networks and SU(2) spin network states.

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