In the U(N)-symmetric sector of the two-vertex loop-quantum-gravity model, the face frames of the twisted-geometry polyhedra evolve by a common scaling plus rotation, so all planar angles stay constant and the polyhedra expand homothetically.
Generating Functions for Coherent Intertwiners
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
We study generating functions for the scalar products of SU(2) coherent intertwiners, which can be interpreted as coherent spin network evaluations on a 2-vertex graph. We show that these generating functions are exactly summable for different choices of combinatorial weights. Moreover, we identify one choice of weight distinguished thanks to its geometric interpretation. As an example of dynamics, we consider the simple case of SU(2) flatness and describe the corresponding Hamiltonian constraint whose quantization on coherent intertwiners leads to partial differential equations that we solve. Furthermore, we generalize explicitly these Wheeler-DeWitt equations for SU(2) flatness on coherent spin networks for arbitrary graphs.
fields
gr-qc 1years
2025 1verdicts
CONDITIONAL 1representative citing papers
citing papers explorer
-
Homothetic expansion of polyhedra in the two-vertex model: emergence of FLRW
In the U(N)-symmetric sector of the two-vertex loop-quantum-gravity model, the face frames of the twisted-geometry polyhedra evolve by a common scaling plus rotation, so all planar angles stay constant and the polyhedra expand homothetically.