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2014

A note on the secondary simplicity constraints in loop quantum gravity

Anzà, Fabio, Speziale, Simone

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A debate has appeared in the literature on loop quantum gravity and spin foams, over whether the secondary simplicity constraints, reducing the connection to be Levi-Civita, should imply the shape matching conditions, reducing twisted geometries to Regge geometries.

We address the question using a simple model with a flat dynamics, in which secondary simplicity constraints arise from a dynamical preservation of the primary ones.
We find that shape matching conditions arise, thus providing support to an affirmative question.
The origin of these extra conditions is to be found in the different graph localisation of the Hamiltonian and primary simplicity constraints.

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