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@ARTICLE{Guedes:1038545,
      author       = {Guedes, Thiago Lucena Macedo and Marugán, Guillermo A.
                      Mena and Müller, Markus and Vidotto, Francesca},
      title        = {{T}aming {T}hiemann's {H}amiltonian constraint in canonical
                      loop quantum gravity: reversibility, eigenstates and
                      graph-change analysis},
      reportid     = {FZJ-2025-01528, arXiv:2412.20272},
      year         = {2025},
      note         = {65 pages, 4 figures},
      abstract     = {The Hamiltonian constraint remains an elusive object in
                      loop quantum gravity because its action on spinnetworks
                      leads to changes in their corresponding graphs. As a result,
                      calculations in loop quantum gravity are often considered
                      unpractical, and neither the eigenstates of the Hamiltonian
                      constraint, which form the physical space of states, nor the
                      concrete effect of its graph-changing character on
                      observables are entirely known. Much worse, there is no
                      reference value to judge whether the commonly adopted
                      graph-preserving approximations lead to results anywhere
                      close to the non-approximated dynamics. Our work sheds light
                      on many of these issues, by devising a new numerical tool
                      that allows us to implement the action of the Hamiltonian
                      constraint without the need for approximations and to
                      calculate expectation values for geometric observables. To
                      achieve that, we fill the theoretical gap left in the
                      derivations of the action of the Hamiltonian constraint on
                      spinnetworks: we provide the first complete derivation of
                      such action for the case of 4-valent spinnetworks, while
                      updating the corresponding derivation for 3-valent
                      spinnetworks. Our derivations also include the action of the
                      volume operator. By proposing a new approach to encode
                      spinnetworks into functions of lists and the derived
                      formulas into functionals, we implement both the Hamiltonian
                      constraint and the volume operator numerically. We are able
                      to transform spinnetworks with graph-changing dynamics
                      perturbatively and verify that volume expectation values
                      have rather different behavior from the approximated,
                      graph-preserving results. Furthermore, using our tool we
                      find a family of potentially relevant solutions of the
                      Hamiltonian constraint. Our work paves the way to a new
                      generation of calculations in loop quantum gravity, in which
                      graph-changing results and their phenomenology can finally
                      be accounted for and understood.},
      cin          = {PGI-2},
      cid          = {I:(DE-Juel1)PGI-2-20110106},
      pnm          = {5221 - Advanced Solid-State Qubits and Qubit Systems
                      (POF4-522)},
      pid          = {G:(DE-HGF)POF4-5221},
      typ          = {PUB:(DE-HGF)25},
      eprint       = {2412.20272},
      howpublished = {arXiv:2412.20272},
      archivePrefix = {arXiv},
      SLACcitation = {$\%\%CITATION$ = $arXiv:2412.20272;\%\%$},
      url          = {https://juser.fz-juelich.de/record/1038545},
}