Physical boundary state for the quantum tetrahedron

Understand

We consider stability under evolution as a criterion to select a physical boundary state for the spinfoam formalism.

• As an example, we apply it to the simplest spinfoam defined by a single quantum tetrahedron and solve the associated eigenvalue problem at leading order in the large spin limit.
• We show that this fixes uniquely the free parameters entering the boundary state.
• Remarkably, the state obtained this way gives a correlation between edges which runs at leading order with the inverse distance between the edges, in agreement with the linearized continuum theory.