A Toy Model to Study the Imposition of the Spin Foam Simplicity Constraints



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12030100

Abstract

We introduce an exactly solvable model to test various proposals for the imposition of the spin foam simplicity constraints. This model is a three-dimensional Holst-Plebanski action for the gauge group SO(4), in which the simplicity constraints mimic the situation of the four-dimensional theory. In particular, the canonical analysis reveals the presence of secondary second class constraints conjugated to the primary ones. We perform the spin foam quantization of the theory in the spirit of the BC and EPRL models, and give arguments for modifying the measure over the holonomies in order to account for the presence of the secondary second class constraints.