  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.
