- Sources
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.
Sources
- Carlo Rovelli and Lee Smolin, [https://arxiv.org/abs/gr-qc/9411005 "Discreteness of Area and Volume in Quantum Gravity", Nuclear Physics B 442, 593 (1995)].
- Abhay Ashtekar and Jerzy Lewandowski, Quantum Theory of Geometry II: Volume operators
1 : Quantum field theory
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