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As a laboratory for loop quantum gravity, we consider the canonicalquantization of the three-dimensional Chern-Simons theory on a noncompact spacewith the topology of a cylinder. Working within the loop quantizationformalism, we define at the quantum level the constraints appearing in thecanonical approach and completely solve them, thus constructing a gauge anddiffeomorphism invariant physical Hilbert space for the theory. This spaceturns out to be infinite dimensional, but separable.

The Hilbert space of Chern-Simons theory on the cylinder. A Loop Quantum Gravity approach