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Nortdita 132:028 ()
We study the question whether it is possible to reformulate the Wilsonian
renormalisation group non-perturbatively directly at the operator (Hamiltonian)
level. Hamiltonian renormalisation would be the natural route to follow if one had
easier access to an interacting Hamiltonian operator rather than to a path
integral, at least in the presence of UV and/or IR cut-off, which is generically
the case in complicated gauge theories such as General Relativity. Our guiding
principle for the definition of the direct Hamiltonian renormalisation group is
that it results in the same continuum theory as the covariant (path integral)
renormalisation group. We will investigate this direct Hamiltonian Renormalisation
for the case of the free massive quantum scalar field and point out its necessity
in a concrete cosmological example for Quantum Gravity.