  In this work we focus on the quantum Einstein-Yang-Mills sector quantised by
the methods of Loop Quantum Gravity (LQG). We point out the improved UV
behaviour of the coupled system as compared to pure quantum Yang-Mills theory
on a fixed, classical background spacetime as was considered in a seminal work
by Kogut and Susskind. Furthermore, we develop a calculational scheme by which
the fundamental spectrum of the quantum Yang-Mills Hamiltonian can be computed
in principle and by which one can make contact to the Wilsonian renormalization
group, possibly purely within the Hamiltonian framework. Finally, we comment on
the relation of the fundamental spectrum to that of pure Yang-Mills theory on a
(flat) classical spacetime.
