The EPRL intertwiners and corrected partition function

Wojciech Kamiski (1) , Marcin Kisielowski (1) , Jerzy Lewandowski (1)

1 Instytut Fizyki Teoretycznej

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 in the general n-valent vertex case for the Barbero-Immirzi parameter less then 1. We find, however, that the EPRL map is not isometric . In the consequence, a partition function can be defined either using the EPRL intertwiners Hilbert product or the SU(2) intertwiners Hilbert product. We use the EPRL one and derive a new, complete formula for the partition function. Next, we view it in terms of the SU(2) intertwiners. The result, however, goes beyond the SU(2) spin-foam models framework and the original EPRL proposal.

Mots clés: Physical Sciences

Wojciech Kamiski, Marcin Kisielowski, Jerzy Lewandowski. The EPRL intertwiners and corrected partition function. Classical and Quantum Gravity, 2010, 27 (16), pp.165020. ⟨10.1088/0264-9381/27/16/165020⟩. ⟨hal-00616260⟩