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Graph coherent states for loop quantum gravity

In this article we further investigate the construction of graph coherent states, first introduced in [1], in the context of loop quantum gravity. We specifically investigate the possibility of defining a family of graph coherent states adapted to the canonical loop quantum gravity Hamiltonian. After discussing various aspects of the general framework and the choice of operators, we use the Euclidean part of the Hamiltonian operator to propose a generator of the generalized canonical structure, necessary to define the coherent states. We then apply the construction procedure, leading to a new family of graph coherent states partially adapted to the gravity Hamiltonian in loop quantum gravity.