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 V: Free Vector Bosons
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
In a recent proposal we applied methods from constructive QFT to derive a Hamiltonian Renormalisation Group in order to employ it ultimately for canonical quantum gravity. The proposal was successfully tested for free scalar fields and thus a natural next step is to test it for free gauge theories. This can be done in the framework of reduced phase space quantisation which allows using techniques developed earlier for scalar field theories. In addition, in canonical quantum gravity one works in representations that support holonomy operators which are ill defined in the Fock representation of say Maxwell or Proca theory. Thus, we consider toy models that have both features, i.e. which employ Fock representations in which holonomy operators are well-defined. We adapt the coarse graining maps considered for scalar fields to those theories for free vector bosons. It turns out that the corresponding fixed pointed theories can be found analytically.
citation-role summary
method 1
citation-polarity summary
fields
gr-qc 1years
2025 1verdicts
CONDITIONAL 1roles
method 1polarities
use method 1representative citing papers
citing papers explorer
-
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.