Stone-von Neumann Theorems in Loop Quantum Gravity

One of the basic steps when quantizing a classical theory is the choice of an appropriate kinematical Hilbert space which the quantized operators are represented on. In quantum mechanics this selection is unique due to the celebrated Stone-von Neumann theorem. Recently, it has been investigated whether similar results may fix both Hilbert space and representation in loop quantum gravity as well. It has turned out that the diffeomorphism invariance of general relativity indeed provides us with strong uniqueness results, as will be discussed in this talk.