Hamiltonian renormalisation IX. U(1)**3 quantum gravity

Abstract

In previous works in this series we focussed on Hamiltonian renormalisation of free field theories in all spacetime dimensions or interacting theories in spacetime dimensions lower than four. In this paper we address the Hamiltonian renormalisation of the U(1)**3 model for Euclidian general relativity in four spacetime dimensions which is self-interacting. The Hamiltonian flow needs as an input a choice of *-algebra and corresponding representation thereof or state on it at each resolution scale. If one uses as input the algebras and states that were used in the recent exact solutions of this model, then one finds that the flow finds as fixed point those exact solution theories.