TL;DR
This paper reviews a new regularization approach for the scalar constraint in Loop Quantum Gravity, highlighting its compatibility with spinfoam models and discussing its advantages and limitations compared to Thiemann's method.
Contribution
It introduces a regularization that enables the scalar constraint to generate Pachner moves and incorporate 15j Wigner symbols, aligning with spinfoam formalism.
Findings
Can generate 1-4 Pachner moves
Contains 15j Wigner symbols in matrix elements
Spoils Thiemann's anomaly-free proof
Abstract
We review a recent proposal for the regularization of the scalar constraint of General Relativity in the context of LQG. The resulting constraint presents strengths and weaknesses compared to Thiemann's prescription. The main improvement is that it can generate the 1-4 Pachner moves and its matrix elements contain 15j Wigner symbols, it is therefore compatible with the spinfoam formalism: the drawback is that Thiemann anomaly free proof is spoiled because the nodes that the constraint creates have volume.
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