# Volume operator

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A quantum field theory of General Relativity provides operators that measure the geometry of space time. The volume operator of a region is defined as the operator that yields the expectation value of a volume measurement of the region , given a state of quantum General Relativity. I.e. is the expectation value for the volume of . Loop Quantum Gravity, for example, provides volume operators, area operators and length operators for regions, surfaces and path respectively.