The EPRL intertwiners and corrected partition function
General Relativity and Quantum Cosmology
2011-09-26 v2 High Energy Physics - Theory
Abstract
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.
Cite
@article{arxiv.0912.0540,
title = {The EPRL intertwiners and corrected partition function},
author = {Wojciech Kamiński and Marcin Kisielowski and Jerzy Lewandowski},
journal= {arXiv preprint arXiv:0912.0540},
year = {2011}
}
Comments
RevTex4, 15 pages, 5 figures; theorem of injectivity of EPRL map corrected