MG11 
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Properties of the Volume Operator in Loop Quantum Gravity

The operator corresponding to the classical volume expression plays a prominent role in Loop Quantum Gravity. Its properties are crucial in order to evaluate the action of the Hamilton constraint operator as well as any description of matter Hamiltonians. Based on (gr-qc/0405060) we have implemented the volume operator of Ashtekar and Lewandowski on a supercomputer, utilizing the Cactus computational framework from numerical relativity. We will present the results of an extensive numerical study, enabling us for the first time to analyze vertices with valence greater than 4. Here not only recoupling theory of the edge spins but also the vertex topology of the graphs underlying the basis states of the quantum theory affect the spectral properties of the operator.