Speaker
Description
Computations in canonical loop quantum gravity are severely hindered by the graph-changing nature of the scalar Hamiltonian constraint. In fact, not even the action of this constraint on 4-valent spin-network vertices has been fully derived in the literature to date. For this reason, drastic approximations, such as graph-non-changing constraints, are usually implemented. In order to overcome this challenge, we derive the complete action of the scalar Euclidean Hamiltonian constraint on 3- and 4-valent vertices, based on which we introduce a new computational method that allows for application of this graph-changing constraint on vertices of arbitrary spins. The method includes no approximations and allows for iterative applications of the constraint on a chosen spin-network vertex, enabling perturbative calculations. Our code also includes a key geometrical observable in loop quantum gravity, the quantum volume. Making use of this new tool, we search for new eigenstates of the constraint. Furthermore, through the numerical calculation of volume expectation values of spin networks, as well as the changes in the expectation values of such observable caused by evolution, we finally provide concrete evidence of the effect of implementing graph-non-changing approximations on the quantum volume, having as reference the action of the complete, graph-changing Euclidean Hamiltonian constraint. Our work represents a new computational milestone in the development of loop quantum gravity, whose numerical power is expected to open new doors for the investigation of the dynamics of spin networks and their geometrical observables in canonical loop quantum gravity.
