Physics:Volume operator
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A quantum field theory of general relativity provides operators that measure the geometry of spacetime. The volume operator [math]\displaystyle{ V(R) }[/math] of a region [math]\displaystyle{ R }[/math] is defined as the operator that yields the expectation value of a volume measurement of the region [math]\displaystyle{ R }[/math], given a state [math]\displaystyle{ \psi }[/math] of quantum General Relativity. I.e.[math]\displaystyle{ \lang \psi, V(R) \psi \rang }[/math] is the expectation value for the volume of [math]\displaystyle{ R }[/math]. 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, "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
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![]() | Original source: https://en.wikipedia.org/wiki/Volume operator.
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