Physical boundary state for the quantum tetrahedron

TL;DR

This paper develops a method to select physical boundary states in spinfoam quantum gravity by analyzing stability under evolution, applying it to a quantum tetrahedron, and demonstrating that the resulting state reproduces expected continuum correlations.

Contribution

It introduces a stability-based criterion for boundary state selection in spinfoam models and applies it to a quantum tetrahedron, deriving a physically consistent correlator.

Findings

The boundary state is uniquely fixed by stability considerations.

The derived correlator matches the inverse distance behavior from continuum theory.

The correlator reflects pure gauge propagation, consistent with 3D gravity.

Abstract

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. Finally, we give an argument why this correlator represents the propagation of a pure gauge, consistently with the absence of physical degrees of freedom in 3d general relativity.