A regularization of the hamiltonian constraint compatible with the spinfoam dynamics

TL;DR

This paper presents a new regularization of Thiemann's Hamiltonian constraint that aligns better with spinfoam dynamics by enabling 1-4 Pachner moves and involves 15j Wigner symbols in its matrix elements.

Contribution

A novel regularization of the Hamiltonian constraint compatible with spinfoam dynamics, capable of generating Pachner moves and incorporating 15j Wigner symbols.

Findings

The new regularization allows 1-4 Pachner moves.

Matrix elements include 15j Wigner symbols.

Enhanced compatibility with spinfoam formalism.

Abstract

We introduce a new regularization for Thiemann's Hamiltonian constraint. The resulting constraint can generate the 1-4 Pachner moves and is therefore more compatible with the dynamics defined by the spinfoam formalism. We calculate its matrix elements and observe the appearence of the 15j Wigner symbol in these.