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arXiv · 0912.0540

The EPRL intertwiners and corrected partition function

Wojciech Kamiński·Marcin Kisielowski·Jerzy Lewandowski
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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.

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Wojciech Kamiński, Marcin Kisielowski, Jerzy Lewandowski. 2011-09-23. The EPRL intertwiners and corrected partition function. https://doi.org/10.1088/0264-9381%2F27%2F16%2F165020

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