For the U(1)^3 toy model, the Hamiltonian renormalisation flow built from Narnhofer-Thirring or Fock inputs has fixed points that coincide with the previously known exact continuum solutions, with explicit convergence estimates for local lattice initial data.
Hamiltonian Renormalisation IV. Renormalisation Flow of D+1 dimensional free scalar fields and Rotation Invariance
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abstract
In this article we extend the test of Hamiltonian Renormalisation proposed in this series of articles to the D-dimensional case using a massive free scalar field. The concepts we introduce are explicitly computed for the D=2 case but transfer immediately to higher dimensions. In this article we define and verify a criterion that monitors, at finite resolution defined by a cubic lattice, whether the flow approaches a rotationally invariant fixed point.
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Hamiltonian renormalisation IX. U(1)**3 quantum gravity
For the U(1)^3 toy model, the Hamiltonian renormalisation flow built from Narnhofer-Thirring or Fock inputs has fixed points that coincide with the previously known exact continuum solutions, with explicit convergence estimates for local lattice initial data.