On the volume simplicity constraint in the EPRL spin foam model

We propose a quantum version of the quadratic volume simplicity constraint for the EPRL spin foam model. It relies on a formula for the volume of 4-dimensional polyhedra, depending on its bivectors and the knotting class of its boundary graph. While this leads to no further condition for the 4-simpl...

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Bibliographic Details
Published in:arXiv.org 2017-10
Main Authors: Bahr, Benjamin, Belov, Vadim
Format: Article
Language:English
Subjects:
Constraint modelling
Online Access:Get full text
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Summary:We propose a quantum version of the quadratic volume simplicity constraint for the EPRL spin foam model. It relies on a formula for the volume of 4-dimensional polyhedra, depending on its bivectors and the knotting class of its boundary graph. While this leads to no further condition for the 4-simplex, the constraint becomes non-trivial for more complicated boundary graphs. We show that, in the semi-classical limit of the hypercuboidal graph, the constraint turns into the geometricity condition observed recently by several authors.
ISSN:2331-8422
DOI:10.48550/arxiv.1710.06195