Loop quantum gravity on non-compact spaces Original Research Article

We present a general procedure for constructing new Hilbert spaces for loop quantum gravity on non-compact spatial manifolds. Given any fixed background state representing a non-compact spatial geometry, we use the Gelʹfand–Naimark–Segal construction to obtain a representation of the algebra of observables. The resulting Hilbert space can be interpreted as describing fluctuations of compact support around this background state. We also give an example of a state which approximates classical flat space and can be used as a background state for our construction.