The EPRL intertwiners and corrected partition function

Details The EPRL intertwiners and corrected partition function The EPRL intertwiners and corrected partition function

2009-12-03

arxiv.org/abs/0912.0540v2

Class.Quant.Grav.27:165020,2010

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

RevTex4, 15 pages, 5 figures; theorem of injectivity of EPRL map corrected

Scientific paper

10.1088/0264-9381/27/16/165020

Do the SU(2) intertwiners parametrize the space of the EPRL solutions to the simplicity constraint? What is a complete form of the partition function written in terms of this parametrization? We prove that the EPRL map is injective for n-valent vertex in case when it is a map from SO(3) into SO(3)xSO(3) representations. We find, however, that the EPRL map is not isometric. In the consequence, in order to be written in a SU(2) amplitude form, the formula for the partition function has to be rederived. We do it and obtain a new, complete formula for the partition function. The result goes beyond the SU(2) spin-foam models framework.

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