Computing the graph-changing dynamics of loop quantum gravity

arXiv (Cornell University)

Abstract

In loop quantum gravity (LQG), states of the gravitational field are represented by labeled graphs called spin networks. Their dynamics can be described by a Hamiltonian constraint, { which acts on the spin network states modifying both spins and graphs.} Fixed-graph approximations of the dynamics have been extensively studied, but its full graph-changing action so far remains elusive. The latter, alongside the solutions of its constraint, are arguably the missing features { in canonical LQG to access phenomenology in all its richness}. Here, we discuss a recently developed numerical tool that, for the first time, implements graph-changing dynamics via the Hamiltonian constraint. We explain how it is used to find new solutions to that constraint and to show that some quantum geometric observables behave differently than in the graph-preserving truncation. We also point out that these new numerical methods can find applications in other domains.

Authors 4

1. Thiago L. M. Guedes Aachen Institute for Quantum Information

   Forschungszentrum Jülich · RWTH Aachen University

   Affiliation as printed

   Institute for Quantum Information , RWTH Aachen University , D-52056 Aachen , Germany

   Peter Grünberg Institute , Theoretical Nanoelectronics , Forschungszentrum Jülich , D-52425 Jülich , Germany

2. Guillermo Antonio Mena Marugán

   Instituto de Estructura de la Materia

   Affiliation as printed

   Instituto de Estructura de la Materia , IEM-CSIC , C/ Serrano 121 , 28006 Madrid , Spain

3. Francesca Vidotto

   Western University · Instituto de Estructura de la Materia

   Affiliation as printed

   Department of Physics and Astronomy , Department of Philosophy , and Rotman Institute , Western University , N6A 5B7 , London , Ontario , Canada

   Instituto de Estructura de la Materia , IEM-CSIC , C/ Serrano 121 , 28006 Madrid , Spain

4. Markus Michael Müller Aachen Institute for Quantum Information

   Forschungszentrum Jülich · RWTH Aachen University

   Affiliation as printed

   Institute for Quantum Information , RWTH Aachen University , D-52056 Aachen , Germany

   Peter Grünberg Institute , Theoretical Nanoelectronics , Forschungszentrum Jülich , D-52425 Jülich , Germany